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Shparlinski, Igor E.

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Author ID: shparlinski.igor-e Recent zbMATH articles by "Shparlinski, Igor E."
Published as: Shparlinski, Igor E.; Shparlinski, Igor; Shparlinskij, I. E.; Shparlinski, I. E.; Shparlinskiĭ, I. E.; Shparlinksi, Igor E.; Shparlinskii, I. E.; Shparlinski, I.; Shparlinski, Igor. E.; Shparlinskij, Igor E.; Spharlinski, Igor E.
Homepage: http://web.maths.unsw.edu.au/~igorshparlinski/
External Links: MGP · ORCID · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef
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Co-Authors

199 single-authored
77 Luca, Florian
63 Banks, William D.
29 Friedlander, John Benjamin
29 Ostafe, Alina
24 von zur Gathen, Joachim
24 Winterhof, Arne
21 Garaev, Moubariz Z.
20 Konyagin, Sergeĭ Vladimirovich
14 Pomerance, Carl Bernard
13 Niederreiter, Harald
13 Sha, Min
10 Gomez-Perez, Domingo
10 Voloch, José Felipe
9 Ahmadi, Omran
9 Bourgain, Jean
9 Gutierrez, Jaime
9 Pappalardi, Francesco
9 Stepanov, Sergei Alexandrovich
8 Karpinski, Marek
8 Lieman, Daniel B.
8 Nguyen, Phong Q.
7 Blackburn, Simon R.
7 Chen, Changhao
7 Cilleruelo, Javier
7 El-Mahassni, Edwin D.
7 Kerr, Bryce
7 Mans, Bernard
7 Mérai, László
6 Chang, Mei-Chu
6 Farashahi, Reza Rezaeian
6 Ford, Kevin B.
6 van der Poorten, Alfred J.
6 Zhang, Tianping
5 Balasuriya, Sanka
5 Bernasconi, Anna
5 Blake, Ian F.
5 Heyman, Randell
5 Lange, Tanja
5 Liu, Kui
5 Mullen, Gary L.
5 Panario, Daniel
5 Steinfeld, Ron
4 Conflitti, Alessandro
4 Damm, Carsten
4 Everest, Graham Robert
4 González Vasco, María Isabel
4 Griffin, Frances
4 Khan, Mizan R.
4 Kohel, David R.
4 Kosachevskaya, L. L.
4 Munsch, Marc
4 Näslund, Mats
4 Shkredov, Il’ya Dmitrievich
4 Sutantyo, Daniel
4 Yau, Kam-hung
4 Zannier, Umberto M.
3 Bordellès, Olivier
3 Broughan, Kevin A.
3 Cohen, Stephen D.
3 Cojocaru, Alina Carmen
3 Dietmann, Rainer
3 Elsholtz, Christian
3 Fouvry, Etienne
3 Kurlberg, Pär
3 Macourt, Simon
3 Menezes, Alfred J.
3 Moree, Pieter
3 Murty, Maruti Ram
3 Romanovtsev, V. V.
3 Silverman, Joseph Hillel
3 Stichtenoth, Henning
3 Sutherland, Andrew V.
3 Wang, Huaxiong
3 Zumalacárregui, Ana
2 Allender, Eric W.
2 Baker, Roger C.
2 Balog, Antal
2 Canetti, Ran
2 Chan, Tsz Ho
2 Contini, Scott
2 Coppersmith, Don
2 D’Andrea, Carlos
2 de la Bretèche, Régis
2 Dewar, Michael C.
2 Dubickas, Artūras
2 Galiev, V. I.
2 Ghioca, Dragos
2 Harcharras, Asma
2 Harman, Glyn
2 Heath-Brown, Roger
2 Howgrave-Graham, Nick A.
2 Larsen, Michael Jeffrey
2 Lenstra, Arjen K.
2 Levieil, Eric
2 Levin, Mordekhaĭ Borisovich
2 Ling, San
2 McGuire, Gary
2 Petridis, Giorgis
2 Polupanov, A. F.
2 Roche-Newton, Oliver
...and 203 more Co-Authors
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Serials

30 Journal of Number Theory
26 Bulletin of the Australian Mathematical Society
25 Proceedings of the American Mathematical Society
21 Acta Arithmetica
20 Mathematics of Computation
20 Finite Fields and their Applications
15 The Quarterly Journal of Mathematics
13 Designs, Codes and Cryptography
11 SIAM Journal on Discrete Mathematics
11 Indagationes Mathematicae. New Series
11 Applicable Algebra in Engineering, Communication and Computing
11 International Journal of Number Theory
10 Information Processing Letters
10 Archiv der Mathematik
10 Mathematika
9 Periodica Mathematica Hungarica
9 Canadian Mathematical Bulletin
9 Glasgow Mathematical Journal
9 Michigan Mathematical Journal
9 Monatshefte für Mathematik
9 IMRN. International Mathematics Research Notices
8 Mathematical Notes
8 Transactions of the American Mathematical Society
8 Experimental Mathematics
7 IEEE Transactions on Information Theory
7 Bulletin of the London Mathematical Society
7 U.S.S.R. Computational Mathematics and Mathematical Physics
7 Bulletin of the Polish Academy of Sciences, Mathematics
7 Journal of Mathematical Cryptology
6 Canadian Journal of Mathematics
6 Mathematische Zeitschrift
6 Uniform Distribution Theory
5 Rocky Mountain Journal of Mathematics
5 Russian Mathematical Surveys
5 Journal of Complexity
5 Computational Complexity
5 Journal de Théorie des Nombres de Bordeaux
5 Mathematical Research Letters
4 Matematicheskie Zametki
4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
4 Colloquium Mathematicum
4 Proceedings of the Edinburgh Mathematical Society. Series II
4 SIAM Journal on Computing
4 Theoretical Computer Science
4 Journal of Symbolic Computation
4 Linear Algebra and its Applications
4 Integers
4 Contemporary Mathematics
3 Journal d’Analyse Mathématique
3 Journal of Mathematical Analysis and Applications
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Problems of Information Transmission
3 Uspekhi Matematicheskikh Nauk [N. S.]
3 Advances in Mathematics
3 Functiones et Approximatio. Commentarii Mathematici
3 Illinois Journal of Mathematics
3 International Journal of Mathematics and Mathematical Sciences
3 Journal of the London Mathematical Society. Second Series
3 Algorithmica
3 Revista Matemática Iberoamericana
3 Journal of Cryptology
3 Mathematics of the USSR, Sbornik
3 Boletín de la Sociedad Matemática Mexicana. Third Series
3 Annals of Combinatorics
3 Revista Matemática Complutense
3 Journal of the Australian Mathematical Society
3 Progress in Computer Science and Applied Logic
3 Advances in Mathematics of Communications
2 Discrete Mathematics
2 Israel Journal of Mathematics
2 Acta Scientiarum Mathematicarum
2 Czechoslovak Mathematical Journal
2 Kodai Mathematical Journal
2 Manuscripta Mathematica
2 Pacific Journal of Mathematics
2 Publicationes Mathematicae
2 Journal of Algorithms
2 European Journal of Combinatorics
2 Applied Mathematics Letters
2 Forum Mathematicum
2 Discrete Mathematics and Applications
2 Problemy Peredachi Informatsii
2 Matematicheskiĭ Sbornik
2 The New York Journal of Mathematics
2 Discrete and Continuous Dynamical Systems
2 The Ramanujan Journal
2 Journal of Integer Sequences
2 Bulletin of the Brazilian Mathematical Society. New Series
2 Pure and Applied Mathematics Quarterly
2 Proceedings of the Steklov Institute of Mathematics
2 Research in the Mathematical Sciences
1 Discrete Applied Mathematics
1 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika
1 Journal of Mathematical Physics
1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
1 Annales des Sciences Mathématiques du Québec
1 The Australian Mathematical Society Gazette
1 Bulletin de la Société Mathématique de France
1 Commentarii Mathematici Helvetici
1 Compositio Mathematica
...and 50 more Serials

Publications by Year

Citations contained in zbMATH Open

542 Publications have been cited 3,209 times in 1,523 Documents Cited by Year
Handbook of finite fields. Zbl 1319.11001
150
2013
Recurrence sequences. Zbl 1033.11006
Everest, Graham; van der Poorten, Alf; Shparlinski, Igor; Ward, Thomas
97
2003
Character sums with exponential functions and their applications. Zbl 0933.11001
Konyagin, S. V.; Shparlinski, I. E.
76
1999
Parameters of integral circulant graphs and periodic quantum dynamics. Zbl 1119.81042
Saxena, Nitin; Severini, Simone; Shparlinski, Igor E.
42
2007
Graphs with integral spectrum. Zbl 1178.05060
Ahmadi, Omran; Alon, Noga; Blake, Ian F.; Shparlinski, Igor E.
40
2009
On the hidden shifted power problem. Zbl 1311.11111
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
32
2012
Finite fields: theory and computation. The meeting point of number theory, computer science, coding theory and cryptography. Zbl 0967.11052
Shparlinski, I. E.
29
1999
Cryptographic applications of analytic number theory. Complexity lower bounds and pseudorandomness. Zbl 1036.94001
Shparlinski, I.
27
2003
Computational and algorithmic problems in finite fields. Zbl 0780.11064
Shparlinski, Igor E.
26
1992
Pseudorandomness and dynamics of Fermat quotients. Zbl 1263.11003
Ostafe, Alina; Shparlinski, Igor E.
25
2011
On the distribution of inversive congruential pseudorandom numbers in parts of the period. Zbl 0983.11048
Niederreiter, Harald; Shparlinski, Igor E.
24
2001
On the concentration of points of polynomial maps and applications. Zbl 1285.11027
Cilleruelo, Javier; Garaev, Moubariz Z.; Ostafe, Alina; Shparlinski, Igor E.
23
2012
On the statistical properties of Diffie-Hellman distributions. Zbl 0997.11066
Canetti, Ran; Friedlander, John; Konyagin, Sergei; Larsen, Michael; Lieman, Daniel; Shparlinski, Igor
23
2000
On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping. Zbl 1038.94007
Coppersmith, Don; Shparlinski, Igor
23
2000
Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height. Zbl 1250.11064
Banks, William D.; Shparlinski, Igor E.
23
2009
The insecurity of the digital signature algorithm with partially known nonces. Zbl 1009.94011
Nguyen, Phong Q.; Shparlinski, Igor E.
22
2002
On the cycle structure of repeated exponentiation modulo a prime. Zbl 1060.11059
Chou, Wun-Seng; Shparlinski, Igor E.
22
2004
On a ternary quadratic form over primes. Zbl 1243.11093
Fouvry, Étienne; Shparlinski, Igor E.
22
2011
Curves with many points and multiplication in finite fields. Zbl 0805.14028
Shparlinski, Igor E.; Tsfasman, Michael A.; Vladut, Serge G.
21
1992
On the divisibility of Fermat quotients. Zbl 1223.11116
Bourgain, Jean; Ford, Kevin; Konyagin, Sergei V.; Shparlinski, Igor E.
21
2010
Recent advances in the theory of nonlinear pseudorandom number generators. Zbl 1076.65008
Niederreiter, Harald; Shparlinski, Igor E.
20
2002
Character sums with exponential functions. Zbl 1017.11045
Friedlander, John B.; Hansen, Jan; Shparlinski, Igor E.
20
2000
Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm. Zbl 1232.11003
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E.
20
2008
The insecurity of the elliptic curve digital signature algorithm with partially known nonces. Zbl 1039.94008
Nguyen, Phong Q.; Shparlinski, Igor E.
19
2003
Modular hyperbolas. Zbl 1272.11050
Shparlinski, Igor E.
19
2012
Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043
Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
19
2002
On exponential sums and group generators for elliptic curves over finite fields. Zbl 1032.11034
Kohel, David R.; Shparlinski, Igor E.
19
2000
On the distribution and lattice structure of nonlinear congruential pseudorandom numbers. Zbl 0942.11037
Niederreiter, Harald; Shparlinski, Igor E.
19
1999
Character sums over integers with restricted \(g\)-ary digits. Zbl 1026.11068
Banks, William D.; Conflitti, Alessandro; Shparlinski, Igor E.
18
2002
Prime numbers with Beatty sequences. Zbl 1167.11010
Banks, William D.; Shparlinski, Igor E.
18
2009
Orders of Gauss periods in finite fields. Zbl 0931.11057
von zur Gathen, Joachim; Shparlinski, Igor
17
1998
On the distribution of the power generator. Zbl 1029.11042
Friedlander, John B.; Shparlinski, Igor E.
17
2001
On the energy of some circulant graphs. Zbl 1083.05029
Shparlinski, Igor
16
2006
On the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1011.11055
Shparlinski, Igor E.
16
2000
Dynamical systems generated by rational functions. Zbl 1030.11072
Niederreiter, Harald; Shparlinski, Igor E.
15
2003
On the distribution of rational functions along a curve over \(\mathbb F_p\) and residue races. Zbl 1068.11043
Granville, Andrew; Shparlinski, Igor E.; Zaharescu, Alexandru
15
2005
On the linear complexity and multidimensional distribution of congruential generators over elliptic curves. Zbl 1116.14307
Hess, Florian; Shparlinski, Igor E.
15
2005
Arithmetic properties of numbers with restricted digits. Zbl 1049.11003
Banks, William D.; Shparlinski, Igor E.
15
2004
Character sums with Fermat quotients. Zbl 1273.11126
Shparlinski, Igor E.
15
2011
Piatetski-Shapiro sequences. Zbl 1327.11062
Baker, Roger C.; Banks, William D.; Brüdern, Jörg; Shparlinski, Igor E.; Weingartner, Andreas J.
15
2013
Exponential sums and rational points on complete intersections. Zbl 0719.11086
Shparlinskij, Igor E.; Skorobogatov, Alexej N.
15
1990
Predicting nonlinear pseudorandom number generators. Zbl 1136.11316
Blackburn, Simon R.; Gomez-Perez, Domingo; Gutierrez, Jaime; Shparlinski, Igor E.
14
2005
On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators. Zbl 1063.65005
Gutierrez, Jaime; Shparlinski, Igor E.; Winterhof, Arne
14
2003
Certain exponential sums and random walks on elliptic curves. Zbl 1068.11078
Lange, Tanja; Shparlinski, Igor E.
14
2005
Bounds of multiplicative character sums with Fermat quotients of primes. Zbl 1221.11004
Shparlinski, Igor E.
14
2011
On congruences with products of variables from short intervals and applications. Zbl 1301.11041
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
14
2013
Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006
Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E.
14
2008
On the distribution of points on multidimensional modular hyperbolas. Zbl 1123.11026
Shparlinski, Igor E.
14
2007
Prescribing the binary digits of squarefree numbers and quadratic residues. Zbl 1431.11015
Dietmann, Rainer; Elsholtz, Christian; Shparlinski, Igor E.
14
2017
On the value set of Fermat quotients. Zbl 1305.11003
Shparlinski, Igor E.
13
2012
On numbers \(n\) dividing the \(n\)th term of a linear recurrence. Zbl 1262.11015
Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E.
13
2012
On Gaussian sums for finite fields and elliptic curves. Zbl 0846.11064
Shparlinski, I. E.
13
1992
Character sums and congruences with \(n!\). Zbl 1060.11046
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
13
2004
Fermat quotients: exponential sums, value set and primitive roots. Zbl 1250.11005
Shparlinski, Igor E.
13
2011
Cancellations amongst Kloosterman sums. Zbl 1368.11092
Shparlinski, Igor E.; Zhang, Tianping
13
2016
Predicting the inversive generator. Zbl 1123.94330
Blackburn, Simon R.; Gomez-Perez, Domingo; Gutierrez, Jaime; Shparlinski, Igor E.
13
2003
On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states. Zbl 1110.81028
Klappenecker, Andreas; Rötteler, Martin; Shparlinski, Igor E.; Winterhof, Arne
13
2005
On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504
Shparlinski, Igor E.; Silverman, Joseph H.
12
2001
On finding primitive roots in finite fields. Zbl 0871.11091
Shparlinski, Igor
12
1996
On the maximal difference between an element and its inverse in residue rings. Zbl 1131.11005
Ford, Kevin; Khan, Mizan R.; Shparlinski, Igor E.; Yankov, Christian L.
12
2005
Exponential sums over Mersenne numbers. Zbl 1060.11045
Banks, William D.; Conflitti, Alessandro; Friedlander, John B.; Shparlinski, Igor E.
12
2004
On the security of Diffie-Hellman bits. Zbl 0997.94548
González Vasco, Maria Isabel; Shparlinski, Igor E.
12
2001
Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average. Zbl 1225.11101
Shparlinski, Igor E.
12
2008
On the distribution of pseudorandom numbers and vectors generated by inversive methods. Zbl 0999.11040
Niederreiter, Harald; Shparlinski, Igor E.
12
2000
Multiplicative order of Gauss periods. Zbl 1201.11110
Ahmadi, Omran; Shparlinski, Igor E.; Voloch, José Felipe
12
2010
On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators. Zbl 1227.11093
Ostafe, Alina; Shparlinski, Igor E.
12
2010
Multiplicative congruences with variables from short intervals. Zbl 1385.11002
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
11
2014
On the spectral Ádám property for circulant graphs. Zbl 1035.05059
Mans, Bernard; Pappalardi, Francesco; Shparlinski, Igor
11
2002
Some doubly exponential sums over \({\mathbb Z}_m\). Zbl 1018.11041
Friedlander, John B.; Konyagin, Sergei; Shparlinski, Igor E.
11
2002
Number theoretic methods in cryptography. Complexity lower bounds. Zbl 0912.11057
Shparlinski, Igor
11
1999
On the consecutive powers of a primitive root: gaps and exponential sums. Zbl 1276.11005
Konyagin, Sergei V.; Shparlinski, Igor E.
11
2012
On group structures realized by elliptic curves over arbitrary finite fields. Zbl 1257.11060
Banks, William D.; Pappalardi, Francesco; Shparlinski, Igor E.
11
2012
On the maximal difference between an element and its inverse modulo \(n\). Zbl 1047.11003
Khan, M. R.; Shparlinski, I. E.
11
2003
Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Zbl 1312.94048
Farashahi, Reza R.; Fouque, Pierre-Alain; Shparlinski, Igor E.; Tibouchi, Mehdi; Voloch, J. Felipe
11
2013
Products in residue classes. Zbl 1182.11046
Friedlander, John B.; Kurlberg, Pär; Shparlinski, Igor E.
11
2008
On the concentration of points on modular hyperbolas and exponential curves. Zbl 1198.11002
Chan, Tsz Ho; Shparlinski, Igor E.
11
2010
On the average energy of circulant graphs. Zbl 1135.05036
Blackburn, Simon R.; Shparlinski, Igor E.
11
2008
On a generalisation of a Lehmer problem. Zbl 1269.11068
Shparlinski, Igor E.
11
2009
Points on curves in small boxes and applications. Zbl 1316.11024
Chang, Mei-Chu; Cilleruelo, Javier; Garaev, Moubariz Z.; Hernández, José; Shparlinski, Igor E.; Zumalacárregui, Ana
10
2014
Divisor problem in arithmetic progressions modulo a prime power. Zbl 1436.11103
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping
10
2018
Counting curves and their projections. Zbl 0990.68642
von zur Gathen, Joachim; Karpinski, Marek; Shparlinski, Igor
10
1997
Smooth orders and cryptographic applications. Zbl 1058.11059
Pomerance, Carl; Shparlinski, Igor E.
10
2002
Prime divisors of sparse integers. Zbl 1049.11010
Shparlinski, I. E.
10
2003
On the solvability of bilinear equations in finite fields. Zbl 1246.11183
Shparlinski, Igor E.
10
2008
On the lower bound of the linear complexity over \(\mathbb F_p\) of Sidelnikov sequences. Zbl 1296.94073
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor; Winterhof, Arne
10
2006
Arithmetic functions on Beatty sequences. Zbl 1227.11045
Abercrombie, Alex G.; Banks, William D.; Shparlinski, Igor E.
10
2009
On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. Zbl 0958.11052
Griffin, Frances; Niederreiter, Harald; Shparlinski, Igor E.
10
1999
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
10
2016
Distribution of matrices with restricted entries over finite fields. Zbl 1181.11030
Ahmadi, Omran; Shparlinski, Igor E.
10
2007
Distribution of some sequences of points on elliptic curves. Zbl 1129.14040
Lange, Tanja; Shparlinski, Igor E.
10
2007
On values taken by the largest prime factor of shifted primes. Zbl 1139.11038
Banks, William D.; Shparlinski, Igor E.
10
2007
On sums of Kloosterman and Gauss sums. Zbl 1453.11105
Shparlinski, Igor E.
9
2019
On the uniformity of distribution of congruential generators over elliptic curves. Zbl 1043.94536
El Mahassni, Edwin; Shparlinski, Igor
9
2002
On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055
Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E.
9
2005
Playing “hide-and-seek” with numbers: the hidden number problem, lattices and exponential sums. Zbl 1208.11134
Shparlinski, Igor E.
9
2005
Pseudorandom number generators from elliptic curves. Zbl 1246.11135
Shparlinski, Igor E.
9
2009
On the number of sign changes of Hecke eigenvalues of newforms. Zbl 1241.11053
Kohnen, Winfried; Lau, Yuk-Kam; Shparlinski, Igor E.
9
2008
On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period. Zbl 1011.11053
Gutierrez, Jaime; Niederreiter, Harald; Shparlinski, Igor E.
9
2000
On the number of various prime divisors of recurrence sequence. Zbl 0635.10006
Shparlinskiĭ, I. E.
9
1987
On the length of critical orbits of stable quadratic polynomials. Zbl 1268.11155
Ostafe, Alina; Shparlinski, Igor E.
9
2010
New bounds of Weyl sums. Zbl 1469.11276
Chen, Changhao; Shparlinski, Igor E.
2
2021
Restricted mean value theorems and the metric theory of restricted Weyl sums. Zbl 1480.11100
Chen, Changhao; Shparlinski, Igor E.
1
2021
On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields. Zbl 1479.11106
Kerr, Bryce; Mello, Jorge; Shparlinski, Igor E.
1
2021
A sparsity result for the dynamical Mordell-Lang conjecture in positive characteristic. Zbl 07438204
Ghioca, Dragos; Ostafe, Alina; Saleh, Sina; Shparlinski, Igor E.
1
2021
Sums of algebraic trace functions twisted by arithmetic functions. Zbl 1469.11267
Korolev, Maxim; Shparlinski, Igor
3
2020
Smooth squarefree and squarefull integers in arithmetic progressions. Zbl 1446.11174
Munsch, Marc; Shparlinski, Igor E.; Yau, Kam Hung
2
2020
On large values of Weyl sums. Zbl 1447.11086
Chen, Changhao; Shparlinski, Igor E.
2
2020
A refinement of the Burgess bound for character sums. Zbl 1471.11229
Kerr, Bryce; Shparlinski, Igor E.; Yau, Kam Hung
2
2020
Average distribution of \(k\)-free numbers in arithmetic progressions. Zbl 1483.11205
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping
2
2020
Unlikely intersections over finite fields: polynomial orbits in small subgroups. Zbl 07147532
Mérai, László; Shparlinski, Igor E.
2
2020
Orders of points in families of elliptic curves. Zbl 1436.11061
Shparlinski, Igor E.
2
2020
Congruences with intervals and arbitrary sets. Zbl 1483.11260
Banks, William; Shparlinski, Igor
2
2020
Hausdorff dimension of the large values of Weyl sums. Zbl 1468.11167
Chen, Changhao; Shparlinski, Igor E.
1
2020
On the structure of graphs of Markoff triples. Zbl 1477.11054
Konyagin, Sergei V.; Makarychev, Sergey V.; Shparlinski, Igor E.; Vyugin, Ilya V.
1
2020
Lower bounds for periods of Ducci sequences. Zbl 1450.11018
Breuer, Florian; Shparlinski, Igor E.
1
2020
On smooth square-free numbers in arithmetic progressions. Zbl 1469.11375
Munsch, Marc; Shparlinski, Igor E.
1
2020
Bounds of trilinear and trinomial exponential sums. Zbl 1452.11017
Macourt, Simon; Petridis, Giorgis; Shkredov, Ilya D.; Shparlinski, Igor E.
1
2020
On the complexity of exact counting of dynamically irreducible polynomials. Zbl 1479.11206
Gómez-Pérez, Domingo; Mérai, László; Shparlinski, Igor E.
1
2020
Distribution of short subsequences of inversive congruential pseudorandom numbers modulo \(2^t\). Zbl 1439.11186
Mérai, László; Shparlinski, Igor E.
1
2020
Value sets of sparse polynomials. Zbl 1453.11163
Shparlinski, Igor E.; Voloch, José Felipe
1
2020
Level curves of rational functions and unimodular points on rational curves. Zbl 1455.11055
Pakovich, Fedor; Shparlinski, Igor E.
1
2020
Kloosterman paths of prime powers moduli. II. Zbl 1456.11233
Ricotta, Guillaume; Royer, Emmanuel; Shparlinski, Igor
1
2020
On sums of Kloosterman and Gauss sums. Zbl 1453.11105
Shparlinski, Igor E.
9
2019
On a sum involving the Euler function. Zbl 1454.11009
Bordellès, Olivier; Dai, Lixia; Heyman, Randell; Pan, Hao; Shparlinski, Igor E.
8
2019
Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems. Zbl 1403.37101
D’Andrea, Carlos; Ostafe, Alina; Shparlinski, Igor E.; Sombra, Martín
8
2019
On multiplicative dependence of values of rational functions and a generalization of the Northcott theorem. Zbl 1442.11142
Ostafe, Alina; Sha, Min; Shparlinski, Igor E.; Zannier, Umberto
4
2019
Cancellations between Kloosterman sums modulo a prime power with prime arguments. Zbl 1441.11192
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping
4
2019
Bounds of trilinear and quadrilinear exponential sums. Zbl 1454.11151
Petridis, Giorgis; Shparlinski, Igor E.
4
2019
On short products of primes in arithmetic progressions. Zbl 1456.11179
Shparlinski, Igor E.
3
2019
On functional graphs of quadratic polynomials. Zbl 1417.05088
Mans, Bernard; Sha, Min; Shparlinski, Igor E.; Sutantyo, Daniel
2
2019
Analogues of the Balog-Wooley decomposition for subsets of finite fields and character sums with convolutions. Zbl 1473.11033
Roche-Newton, Oliver; Shparlinski, Igor E.; Winterhof, Arne
2
2019
Bounds on short character sums and \(L\)-functions with characters to a powerful modulus. Zbl 1460.11110
Banks, William D.; Shparlinski, Igor E.
2
2019
Disjointness of the Möbius transformation and Möbius function. Zbl 1454.11147
El Abdalaoui, El Houcein; Shparlinski, Igor E.
1
2019
Double sums of Kloosterman sums in finite fields. Zbl 1447.11117
Macourt, Simon; Shparlinski, Igor E.
1
2019
On the typical size and cancellations among the coefficients of some modular forms. Zbl 1450.11100
Luca, Florian; Radziwiłł, Maksym; Shparlinski, Igor E.
1
2019
Counting integers with a smooth totient. Zbl 1475.11177
Banks, W. D.; Friedlander, J. B.; Pomerance, C.; Shparlinski, I. E.
1
2019
Divisor problem in arithmetic progressions modulo a prime power. Zbl 1436.11103
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping
10
2018
Multiplicative energy of shifted subgroups and bounds on exponential sums with trinomials in finite fields. Zbl 1448.11213
Macourt, Simon; Shkredov, Ilya D.; Shparlinski, Igor E.
7
2018
Multiplicative orders in orbits of polynomials over finite fields. Zbl 1431.11130
Shparlinski, Igor E.
5
2018
On multiplicatively dependent vectors of algebraic numbers. Zbl 1442.11134
Pappalardi, Francesco; Sha, Min; Shparlinski, Igor E.; Stewart, Cameron L.
4
2018
Orbits of polynomial dynamical systems modulo primes. Zbl 1416.37081
Chang, Mei-Chu; D’Andrea, Carlos; Ostafe, Alina; Shparlinski, Igor E.; Sombra, Martín
3
2018
On abelian multiplicatively dependent points on a curve in a torus. Zbl 1440.11101
Ostafe, Alina; Sha, Min; Shparlinski, Igor E.; Zannier, Umberto
2
2018
Linear equations with rational fractions of bounded height and stochastic matrices. Zbl 1422.11069
Shparlinski, Igor E.
2
2018
Elliptic curves in isogeny classes. Zbl 1444.11122
Shparlinski, Igor E.; Zhao, Liangyi
2
2018
Trilinear forms with double Kloosterman sums. Zbl 1447.11089
Shparlinski, Igor E.
2
2018
Bilinear forms with exponential sums with binomials. Zbl 1429.11069
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping
2
2018
Polynomial interpolation and identity testing from high powers over finite fields. Zbl 1390.11128
Ivanyos, Gábor; Karpinski, Marek; Santha, Miklos; Saxena, Nitin; Shparlinski, Igor E.
2
2018
The Sato-Tate distribution in thin parametric families of elliptic curves. Zbl 1426.11057
de la Bretèche, Régis; Sha, Min; Shparlinski, Igor E.; Voloch, José Felipe
2
2018
Connected components of the graph generated by power maps in prime finite fields. Zbl 1441.05108
Pomerance, Carl; Shparlinksi, Igor E.
1
2018
Double character sums with intervals and arbitrary sets. Zbl 1459.11166
Shkredov, Ilya D.; Shparlinski, Igor E.
1
2018
Denominators of Bernoulli polynomials. Zbl 1415.11121
Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
1
2018
On the error term of a lattice counting problem. Zbl 1380.11085
Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E.
1
2018
Prescribing the binary digits of squarefree numbers and quadratic residues. Zbl 1431.11015
Dietmann, Rainer; Elsholtz, Christian; Shparlinski, Igor E.
14
2017
Orbits of algebraic dynamical systems in subgroups and subfields. Zbl 1393.37113
Ostafe, Alina; Shparlinski, Igor E.
7
2017
Squares in Piatetski-Shapiro sequences. Zbl 1428.11051
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping
5
2017
On some multiple character sums. Zbl 1427.11078
Shkredov, Ilya D.; Shparlinski, Igor E.
3
2017
Double exponential sums with exponential functions. Zbl 1428.11143
Shparlinski, Igor E.; Yau, Kam Hung
3
2017
On distances in lattices from algebraic number fields. Zbl 1433.11083
Dubickas, Artūras; Sha, Min; Shparlinski, Igor E.
2
2017
The Sato-Tate distribution in families of elliptic curves with a rational parameter of bounded height. Zbl 1410.11054
Sha, Min; Shparlinski, Igor E.
2
2017
Power series approximations to Fekete polynomials. Zbl 1427.11030
Bell, Jason; Shparlinski, Igor E.
2
2017
On two functions arising in the study of the Euler and Carmichael quotients. Zbl 1425.11009
Luca, Florian; Sha, Min; Shparlinski, Igor E.
1
2017
Cancellations amongst Kloosterman sums. Zbl 1368.11092
Shparlinski, Igor E.; Zhang, Tianping
13
2016
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
10
2016
Products of small integers in residue classes and additive properties of Fermat quotients. Zbl 1414.11109
Harman, Glyn; Shparlinski, Igor E.
6
2016
Almost primes of the form \(\lfloor p^c \rfloor\). Zbl 1355.11099
Banks, William D.; Guo, Victor Z.; Shparlinski, Igor E.
4
2016
Bounds of double multiplicative character sums and gaps between residues of exponential functions. Zbl 1419.11004
Shparlinski, Igor E.; Yau, Kam-hung
4
2016
On the additive energy of the distance set in finite fields. Zbl 1403.11078
Shparlinski, Igor E.
4
2016
Cyclotomic coefficients: gaps and jumps. Zbl 1405.11032
Camburu, Oana-Maria; Ciolan, Emil-Alexandru; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
4
2016
Counting co-cyclic lattices. Zbl 1348.11056
Nguyen, Phong Q.; Shparlinski, Igor E.
4
2016
Linear congruences with ratios. Zbl 1383.11041
Shparlinski, Igor E.
3
2016
Groups generated by iterations of polynomials over finite fields. Zbl 1347.11084
Shparlinski, Igor E.
3
2016
Upper and lower bounds for higher moments of theta functions. Zbl 1409.11034
Munsch, Marc; Shparlinski, Igor E.
3
2016
Polynomial values in small subgroups of finite fields. Zbl 1407.11051
Shparlinski, Igor E.
3
2016
Fractional parts of Dedekind sums. Zbl 1419.11072
Banks, William D.; Shparlinski, Igor E.
2
2016
On small gaps between the elements of multiplicative subgroups of finite fields. Zbl 1367.11040
Shparlinski, Igor E.
2
2016
Averaging operators over homogeneous varieties over finite fields. Zbl 1346.43002
Koh, Doowon; Shen, Chun-Yen; Shparlinski, Igor
1
2016
Ratios of small integers in multiplicative subgroups of residue rings. Zbl 1403.11062
Shparlinski, Igor E.
1
2016
Dynamical systems of non-algebraic origin: fixed points and orbit lengths. Zbl 1420.37119
Shparlinski, Igor E.
1
2016
On bilinear exponential and character sums with reciprocals of polynomials. Zbl 1400.11123
Shparlinski, Igor E.
1
2016
Counting irreducible binomials over finite fields. Zbl 1371.11150
Heyman, Randell; Shparlinski, Igor E.
1
2016
Subgroups generated by rational functions in finite fields. Zbl 1395.11071
Gómez-Pérez, Domingo; Shparlinski, Igor E.
5
2015
On the fixed points of the map \(x \mapsto x^x\) modulo a prime. Zbl 1393.11029
Kurlberg, Pär; Luca, Florian; Shparlinski, Igor E.
5
2015
Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153
Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E.
5
2015
Polynomial values in subfields and affine subspaces of finite fields. Zbl 1396.11016
Roche-Newton, Oliver; Shparlinski, Igor E.
4
2015
Quadratic non-residues in short intervals. Zbl 1378.11012
Konyagin, Sergei V.; Shparlinski, Igor E.
4
2015
Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves. Zbl 1384.11033
Sha, Min; Shparlinski, Igor E.
4
2015
Congruences with intervals and subgroups modulo a prime. Zbl 1379.11004
Munsch, Marc; Shparlinski, Igor E.
3
2015
Explicit form of Cassels’ \(p\)-adic embedding theorem for number fields. Zbl 1326.11062
Dubickas, Arturas; Sha, Min; Shparlinski, Igor
2
2015
Cayley graphs generated by small degree polynomials over finite fields. Zbl 1311.05083
Shparlinski, Igor E.
2
2015
On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average. Zbl 1400.11164
Shparlinski, Igor E.; Sutherland, Andrew V.
2
2015
On the product of small Elkies primes. Zbl 1317.11061
Shparlinski, Igor E.
1
2015
Counting additive decompositions of quadratic residues in finite fields. Zbl 1393.11006
Blackburn, Simon R.; Konyagin, Sergei V.; Shparlinski, Igor E.
1
2015
Close values of shifted modular inversions and the decisional modular inversion hidden number problem. Zbl 1369.11100
Shparlinski, Igor E.
1
2015
Distribution of polynomial discriminants modulo a prime. Zbl 1364.11153
Shparlinski, Igor E.
1
2015
Multiplicative congruences with variables from short intervals. Zbl 1385.11002
Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E.
11
2014
Points on curves in small boxes and applications. Zbl 1316.11024
Chang, Mei-Chu; Cilleruelo, Javier; Garaev, Moubariz Z.; Hernández, José; Shparlinski, Igor E.; Zumalacárregui, Ana
10
2014
On irreducible divisors of iterated polynomials. Zbl 1339.11099
Gómez-Pérez, Domingo; Ostafe, Alina; Shparlinski, Igor E.
6
2014
Double character sums over subgroups and intervals. Zbl 1316.11076
Chang, Mei-Chu; Shparlinski, Igor E.
5
2014
Elements of large order on varieties over prime finite fields. Zbl 1366.11084
Chang, Mei-Chu; Kerr, Bryce; Shparlinski, Igor E.; Zannier, Umberto
5
2014
On the distribution of Atkin and Elkies primes. Zbl 1312.11048
Shparlinski, Igor E.; Sutherland, Andrew V.
5
2014
...and 442 more Documents
all top 5

Cited by 1,466 Authors

290 Shparlinski, Igor E.
68 Luca, Florian
55 Winterhof, Arne
28 Ostafe, Alina
26 Garaev, Moubariz Z.
23 Banks, William D.
21 Shkredov, Il’ya Dmitrievich
19 Sha, Min
18 Chen, Zhixiong
16 Chang, Mei-Chu
16 Mérai, László
16 von zur Gathen, Joachim
15 Bourgain, Jean
15 Gomez-Perez, Domingo
15 Konyagin, Sergeĭ Vladimirovich
14 Cilleruelo, Javier
14 Niederreiter, Harald
13 Ballet, Stéphane
13 Koh, Doowon
13 Korolëv, Maksim Aleksandrovich
13 Meidl, Wilfried
13 Vinh, Le Anh
12 Ahmadi, Omran
12 Panario, Daniel
11 Bell, Jason P.
11 Dubickas, Artūras
11 Sanna, Carlo
10 Bašić, Milan
10 Gutierrez, Jaime
10 Kerr, Bryce
9 Farashahi, Reza Rezaeian
9 Ford, Kevin B.
9 Friedlander, John Benjamin
9 Munsch, Marc
9 Zaharescu, Alexandru
9 Zhang, Wenpeng
8 Cochrane, Todd
8 Gómez, Domingo
8 Pham Van Thang
8 Pollack, Paul
8 Zhang, Tianping
7 Ilić, Aleksandar
7 Macourt, Simon
7 Moree, Pieter
7 Voloch, José Felipe
7 Yau, Kam-hung
6 Baier, Stephan
6 Blake, Ian F.
6 Cojocaru, Alina Carmen
6 Dartyge, Cécile
6 Du, Xiaoni
6 Galbraith, Steven D.
6 Gao, Shuhong
6 García, Victor Cuauhtemoc
6 Karpinski, Marek
6 Lv, Xingxing
6 Micheli, Giacomo
6 Murty, Maruti Ram
6 Pappalardi, Francesco
6 Reis, Lucas
6 Sander, Jürgen W.
6 Shen, Chun-Yen
6 Shteĭnikov, Yuriĭ Nikolaevich
6 Tibouchi, Mehdi
6 Topuzoǧlu, Alev
6 Wan, Daqing
5 Aly, Hassan Y.
5 Cao, Xiwang
5 Cheng, Qi
5 Cohen, Stephen D.
5 El-Mahassni, Edwin D.
5 Harvey, David I.
5 Ibeas, Álvar
5 Jones, Rafe
5 Lange, Tanja
5 Mauduit, Christian
5 Mefenza, Thierry
5 Mkaouar, Mohamed
5 Petridis, Giorgis
5 Pieltant, Julia
5 Pomerance, Carl Bernard
5 Sárközy, András
5 Shani, Barak
5 Silverman, Joseph Hillel
5 Vergnaud, Damien
5 Ward, Thomas B.
5 Wu, Chenhuang
5 Yi, Yuan
5 Zumalacárregui, Ana
4 Blackburn, Simon R.
4 Chen, Changhao
4 Chen, Yonggao
4 Cusick, Thomas W.
4 Dietmann, Rainer
4 Elsholtz, Christian
4 Erdélyi, Tamás
4 Garton, Derek
4 Goryashin, Dmitriĭ Viktorovich
4 Grau, José María
4 Grigor’ev, Dmitriĭ Yur’evich
...and 1,366 more Authors
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Cited in 231 Serials

124 Journal of Number Theory
93 Finite Fields and their Applications
52 Designs, Codes and Cryptography
50 International Journal of Number Theory
47 Mathematics of Computation
46 Proceedings of the American Mathematical Society
42 Bulletin of the Australian Mathematical Society
30 Linear Algebra and its Applications
29 Monatshefte für Mathematik
29 Journal of Symbolic Computation
28 Acta Arithmetica
27 Information Processing Letters
25 Mathematical Notes
23 Applicable Algebra in Engineering, Communication and Computing
20 Discrete Applied Mathematics
19 Theoretical Computer Science
18 Transactions of the American Mathematical Society
18 Journal of Complexity
18 Indagationes Mathematicae. New Series
17 Periodica Mathematica Hungarica
17 Proceedings of the Steklov Institute of Mathematics
16 The Ramanujan Journal
15 Israel Journal of Mathematics
15 Mathematika
15 Journal de Théorie des Nombres de Bordeaux
14 Journal of Mathematical Cryptology
13 Journal of Algebra
13 Experimental Mathematics
13 Integers
13 Cryptography and Communications
12 Archiv der Mathematik
12 Functiones et Approximatio. Commentarii Mathematici
12 Mathematische Zeitschrift
10 Comptes Rendus. Mathématique. Académie des Sciences, Paris
10 Advances in Mathematics of Communications
9 Discrete Mathematics
9 Linear and Multilinear Algebra
9 Chebyshevskiĭ Sbornik
9 Journal of Mathematics
8 Rocky Mountain Journal of Mathematics
8 Canadian Mathematical Bulletin
8 Acta Mathematica Hungarica
8 Revista Matemática Iberoamericana
8 Acta Mathematica Sinica. English Series
8 Matematicheskie Voprosy Kriptografii
7 Journal d’Analyse Mathématique
7 Advances in Mathematics
7 Glasgow Mathematical Journal
7 Michigan Mathematical Journal
7 SIAM Journal on Discrete Mathematics
7 Forum Mathematicum
7 Journal of the Australian Mathematical Society
7 Research in Number Theory
6 Applied Mathematics and Computation
6 Mathematische Annalen
6 Applied Mathematics Letters
6 Journal of Mathematical Sciences (New York)
6 Science China. Mathematics
5 Indian Journal of Pure & Applied Mathematics
5 Journal of Mathematical Analysis and Applications
5 Journal of Mathematical Physics
5 Mathematical Proceedings of the Cambridge Philosophical Society
5 Inventiones Mathematicae
5 European Journal of Combinatorics
5 Algorithmica
5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
5 Computational Complexity
5 The Electronic Journal of Combinatorics
5 Wuhan University Journal of Natural Sciences (WUJNS)
5 LMS Journal of Computation and Mathematics
5 Quantum Information Processing
4 Lithuanian Mathematical Journal
4 Duke Mathematical Journal
4 Journal of Combinatorial Theory. Series A
4 Journal of Pure and Applied Algebra
4 Quaestiones Mathematicae
4 Journal of Cryptology
4 Journal of Inequalities and Applications
4 Annals of Combinatorics
4 Journal of Discrete Mathematical Sciences & Cryptography
4 Forum of Mathematics, Sigma
4 Research in the Mathematical Sciences
3 Computers & Mathematics with Applications
3 Czechoslovak Mathematical Journal
3 Information Sciences
3 Journal of Computer and System Sciences
3 Journal of Functional Analysis
3 Manuscripta Mathematica
3 Pacific Journal of Mathematics
3 Proceedings of the Edinburgh Mathematical Society. Series II
3 The New York Journal of Mathematics
3 The Journal of Fourier Analysis and Applications
3 Taiwanese Journal of Mathematics
3 Journal of the European Mathematical Society (JEMS)
3 Journal of Systems Science and Complexity
3 International Journal of Quantum Information
3 Science China. Information Sciences
3 AIMS Mathematics
2 Moscow University Mathematics Bulletin
2 Problems of Information Transmission
...and 131 more Serials
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Cited in 45 Fields

1,202 Number theory (11-XX)
256 Information and communication theory, circuits (94-XX)
166 Combinatorics (05-XX)
137 Computer science (68-XX)
117 Algebraic geometry (14-XX)
68 Dynamical systems and ergodic theory (37-XX)
56 Numerical analysis (65-XX)
51 Field theory and polynomials (12-XX)
46 Group theory and generalizations (20-XX)
38 Linear and multilinear algebra; matrix theory (15-XX)
31 Quantum theory (81-XX)
30 Commutative algebra (13-XX)
17 Probability theory and stochastic processes (60-XX)
14 Harmonic analysis on Euclidean spaces (42-XX)
12 Convex and discrete geometry (52-XX)
11 Order, lattices, ordered algebraic structures (06-XX)
9 Functions of a complex variable (30-XX)
9 Functional analysis (46-XX)
8 Mathematical logic and foundations (03-XX)
6 Associative rings and algebras (16-XX)
6 Real functions (26-XX)
6 Special functions (33-XX)
5 Topological groups, Lie groups (22-XX)
5 Approximations and expansions (41-XX)
5 Abstract harmonic analysis (43-XX)
5 Geometry (51-XX)
4 Statistical mechanics, structure of matter (82-XX)
4 Biology and other natural sciences (92-XX)
3 History and biography (01-XX)
3 Nonassociative rings and algebras (17-XX)
3 Measure and integration (28-XX)
3 Operator theory (47-XX)
3 Operations research, mathematical programming (90-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Ordinary differential equations (34-XX)
2 Partial differential equations (35-XX)
2 Difference and functional equations (39-XX)
2 Algebraic topology (55-XX)
2 Statistics (62-XX)
1 Category theory; homological algebra (18-XX)
1 Sequences, series, summability (40-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 General topology (54-XX)
1 Fluid mechanics (76-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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