Hauck, Maximilian; Shparlinski, Igor E. Smooth numbers with few nonzero binary digits. (English) Zbl 07802118 Can. Math. Bull. 67, No. 1, 74-89 (2024). MSC: 11A63 11L40 11N25 PDFBibTeX XMLCite \textit{M. Hauck} and \textit{I. E. Shparlinski}, Can. Math. Bull. 67, No. 1, 74--89 (2024; Zbl 07802118) Full Text: DOI arXiv
Fouvry, Étienne; Shparlinski, Igor E. On character sums with determinants. (English) Zbl 07786154 Sci. China, Math. 66, No. 12, 2693-2714 (2023). Reviewer: Mehdi Hassani (Zanjan) MSC: 11L40 11N25 PDFBibTeX XMLCite \textit{É. Fouvry} and \textit{I. E. Shparlinski}, Sci. China, Math. 66, No. 12, 2693--2714 (2023; Zbl 07786154) Full Text: DOI arXiv
Garaev, Moubariz Z.; Shparlinski, Igor E. On the distribution of modular inverses from short intervals. (English) Zbl 07754842 Mathematika 69, No. 4, 1183-1194 (2023). MSC: 11J71 11K38 11L05 11N25 PDFBibTeX XMLCite \textit{M. Z. Garaev} and \textit{I. E. Shparlinski}, Mathematika 69, No. 4, 1183--1194 (2023; Zbl 07754842) Full Text: DOI arXiv OA License
Banks, William; Shparlinski, Igor On a conjecture of Soundararajan. (English) Zbl 1523.11166 Bull. Lond. Math. Soc. 54, No. 1, 301-317 (2022). MSC: 11N25 11N69 11M20 PDFBibTeX XMLCite \textit{W. Banks} and \textit{I. Shparlinski}, Bull. Lond. Math. Soc. 54, No. 1, 301--317 (2022; Zbl 1523.11166) Full Text: DOI arXiv
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping Average distribution of \(k\)-free numbers in arithmetic progressions. (English) Zbl 1483.11205 Math. Nachr. 293, No. 8, 1505-1514 (2020). MSC: 11N25 11N13 11B25 11N37 PDFBibTeX XMLCite \textit{K. Liu} et al., Math. Nachr. 293, No. 8, 1505--1514 (2020; Zbl 1483.11205) Full Text: DOI
Kerr, Bryce; Shparlinski, Igor E.; Yau, Kam Hung A refinement of the Burgess bound for character sums. (English) Zbl 1471.11229 Mich. Math. J. 69, No. 2, 227-240 (2020). Reviewer: Arjun Singh Chetry (Guwahati) MSC: 11L40 11N25 PDFBibTeX XMLCite \textit{B. Kerr} et al., Mich. Math. J. 69, No. 2, 227--240 (2020; Zbl 1471.11229) Full Text: DOI arXiv Euclid
Munsch, Marc; Shparlinski, Igor E. On smooth square-free numbers in arithmetic progressions. (English) Zbl 1469.11375 J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041-1067 (2020). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N25 11B25 11L40 PDFBibTeX XMLCite \textit{M. Munsch} and \textit{I. E. Shparlinski}, J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041--1067 (2020; Zbl 1469.11375) Full Text: DOI arXiv
Munsch, Marc; Shparlinski, Igor E.; Yau, Kam Hung Smooth squarefree and squarefull integers in arithmetic progressions. (English) Zbl 1446.11174 Mathematika 66, No. 1, 56-70 (2020). Reviewer: Krassimir Atanassov (Sofia) MSC: 11N25 11B25 11L05 11L40 PDFBibTeX XMLCite \textit{M. Munsch} et al., Mathematika 66, No. 1, 56--70 (2020; Zbl 1446.11174) Full Text: DOI arXiv
Korolev, Maxim; Shparlinski, Igor Sums of algebraic trace functions twisted by arithmetic functions. (English) Zbl 1469.11267 Pac. J. Math. 304, No. 2, 505-522 (2020). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11L05 11N25 11T23 PDFBibTeX XMLCite \textit{M. Korolev} and \textit{I. Shparlinski}, Pac. J. Math. 304, No. 2, 505--522 (2020; Zbl 1469.11267) Full Text: DOI arXiv
Banks, W. D.; Friedlander, J. B.; Pomerance, C.; Shparlinski, I. E. Counting integers with a smooth totient. (English) Zbl 1475.11177 Q. J. Math. 70, No. 4, 1371-1386 (2019). Reviewer: József Sándor (Cluj-Napoca) MSC: 11N60 11N25 11N64 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Q. J. Math. 70, No. 4, 1371--1386 (2019; Zbl 1475.11177) Full Text: DOI arXiv
Shparlinski, Igor E. On short products of primes in arithmetic progressions. (English) Zbl 1456.11179 Proc. Am. Math. Soc. 147, No. 3, 977-986 (2019). MSC: 11N25 11B25 11L07 11N36 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 147, No. 3, 977--986 (2019; Zbl 1456.11179) Full Text: DOI arXiv
Pappalardi, Francesco; Sha, Min; Shparlinski, Igor E.; Stewart, Cameron L. On multiplicatively dependent vectors of algebraic numbers. (English) Zbl 1442.11134 Trans. Am. Math. Soc. 370, No. 9, 6221-6244 (2018). MSC: 11N25 11R04 PDFBibTeX XMLCite \textit{F. Pappalardi} et al., Trans. Am. Math. Soc. 370, No. 9, 6221--6244 (2018; Zbl 1442.11134) Full Text: DOI arXiv
Shparlinski, Igor E. Character sums with smooth numbers. (English) Zbl 1415.11113 Arch. Math. 110, No. 5, 467-476 (2018). Reviewer: Olivier Ramaré (Marseille) MSC: 11L40 11N25 11N36 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Arch. Math. 110, No. 5, 467--476 (2018; Zbl 1415.11113) Full Text: DOI arXiv
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping Divisor problem in arithmetic progressions modulo a prime power. (English) Zbl 1436.11103 Adv. Math. 325, 459-481 (2018). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11L05 11N25 11N37 11T23 PDFBibTeX XMLCite \textit{K. Liu} et al., Adv. Math. 325, 459--481 (2018; Zbl 1436.11103) Full Text: DOI arXiv
Dietmann, Rainer; Elsholtz, Christian; Shparlinski, Igor E. Prescribing the binary digits of squarefree numbers and quadratic residues. (English) Zbl 1431.11015 Trans. Am. Math. Soc. 369, No. 12, 8369-8388 (2017). MSC: 11A63 11B30 11N25 11H06 11L40 11P70 11T30 PDFBibTeX XMLCite \textit{R. Dietmann} et al., Trans. Am. Math. Soc. 369, No. 12, 8369--8388 (2017; Zbl 1431.11015) Full Text: DOI arXiv
Rivat, Joël; Shparlinski, Igor E. Multiples of squares in short intervals. (English) Zbl 1407.11112 Funct. Approximatio, Comment. Math. 54, No. 1, 57-63 (2016). MSC: 11N25 PDFBibTeX XMLCite \textit{J. Rivat} and \textit{I. E. Shparlinski}, Funct. Approximatio, Comment. Math. 54, No. 1, 57--63 (2016; Zbl 1407.11112) Full Text: DOI Euclid
Harman, Glyn; Shparlinski, Igor E. Products of small integers in residue classes and additive properties of Fermat quotients. (English) Zbl 1414.11109 Int. Math. Res. Not. 2016, No. 5, 1424-1446 (2016). MSC: 11N25 PDFBibTeX XMLCite \textit{G. Harman} and \textit{I. E. Shparlinski}, Int. Math. Res. Not. 2016, No. 5, 1424--1446 (2016; Zbl 1414.11109) Full Text: DOI arXiv
Banks, William D.; Guo, Victor Z.; Shparlinski, Igor E. Almost primes of the form \(\lfloor p^c \rfloor\). (English) Zbl 1355.11099 Indag. Math., New Ser. 27, No. 2, 423-436 (2016). Reviewer: A. Sankaranarayanan (Mumbai) MSC: 11N80 11N25 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Indag. Math., New Ser. 27, No. 2, 423--436 (2016; Zbl 1355.11099) Full Text: DOI arXiv
Camburu, Oana-Maria; Ciolan, Emil-Alexandru; Luca, Florian; Moree, Pieter; Shparlinski, Igor E. Cyclotomic coefficients: gaps and jumps. (English) Zbl 1405.11032 J. Number Theory 163, 211-237 (2016). MSC: 11C08 11B83 11L07 11N25 PDFBibTeX XMLCite \textit{O.-M. Camburu} et al., J. Number Theory 163, 211--237 (2016; Zbl 1405.11032) Full Text: DOI arXiv
Shparlinski, Igor E. Squarefree parts of discriminants of trinomials. (English) Zbl 1316.11083 Arch. Math. 102, No. 6, 545-554 (2014). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11N25 11N36 11L40 11C08 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Arch. Math. 102, No. 6, 545--554 (2014; Zbl 1316.11083) Full Text: DOI
Shparlinski, Igor E. Evasive properties of sparse graphs and some linear equations in primes. (English) Zbl 1420.05092 Theor. Comput. Sci. 547, 117-121 (2014). MSC: 05C42 11Z05 11N25 11N13 68Q25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Theor. Comput. Sci. 547, 117--121 (2014; Zbl 1420.05092) Full Text: DOI arXiv
Shparlinski, Igor E.; Sutantyo, Daniel Distribution of elliptic twin primes in isogeny and isomorphism classes. (English) Zbl 1317.11097 J. Number Theory 137, 1-15 (2014). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11N25 11G20 11T71 14H52 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{D. Sutantyo}, J. Number Theory 137, 1--15 (2014; Zbl 1317.11097) Full Text: DOI
Dietmann, Rainer; Elsholtz, Christian; Shparlinski, Igor E. On gaps between primitive roots in the Hamming metric. (English) Zbl 1282.11123 Q. J. Math. 64, No. 4, 1043-1055 (2013). MSC: 11N25 11A07 PDFBibTeX XMLCite \textit{R. Dietmann} et al., Q. J. Math. 64, No. 4, 1043--1055 (2013; Zbl 1282.11123) Full Text: DOI arXiv
Harvey, David; Shparlinski, Igor E. Statistics of different reduction types of Fermat curves. (English) Zbl 1368.11057 Exp. Math. 22, No. 3, 243-249 (2013). MSC: 11G20 11N25 11Y40 PDFBibTeX XMLCite \textit{D. Harvey} and \textit{I. E. Shparlinski}, Exp. Math. 22, No. 3, 243--249 (2013; Zbl 1368.11057) Full Text: DOI arXiv
Shparlinski, Igor E. On vanishing Fermat quotients and a bound of the Ihara sum. (English) Zbl 1315.11004 Kodai Math. J. 36, No. 1, 99-108 (2013). Reviewer: Florian Luca (Morelia) MSC: 11A07 11N25 11R04 11R18 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Kodai Math. J. 36, No. 1, 99--108 (2013; Zbl 1315.11004) Full Text: DOI arXiv Euclid
Baker, Roger C.; Banks, William D.; Brüdern, Jörg; Shparlinski, Igor E.; Weingartner, Andreas J. Piatetski-Shapiro sequences. (English) Zbl 1327.11062 Acta Arith. 157, No. 1, 37-68 (2013). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11L07 PDFBibTeX XMLCite \textit{R. C. Baker} et al., Acta Arith. 157, No. 1, 37--68 (2013; Zbl 1327.11062) Full Text: DOI arXiv
Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E. On numbers \(n\) dividing the \(n\)th term of a linear recurrence. (English) Zbl 1262.11015 Proc. Edinb. Math. Soc., II. Ser. 55, No. 2, 271-289 (2012). Reviewer: Chris Smyth (Edinburgh) MSC: 11B37 11A07 11N25 PDFBibTeX XMLCite \textit{J. J. Alba González} et al., Proc. Edinb. Math. Soc., II. Ser. 55, No. 2, 271--289 (2012; Zbl 1262.11015) Full Text: DOI arXiv
Shparlinski, Igor E. On the restricted divisor function in arithmetic progressions. (English) Zbl 1323.11073 Rev. Mat. Iberoam. 28, No. 1, 231-238 (2012). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11N37 11N56 11N25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Rev. Mat. Iberoam. 28, No. 1, 231--238 (2012; Zbl 1323.11073) Full Text: DOI arXiv
Fouvry, Étienne; Shparlinski, Igor E. Smooth shifted monomial products. (English) Zbl 1249.11095 Publ. Math. Debr. 79, No. 3-4, 423-432 (2011). MSC: 11N25 11L40 11N36 PDFBibTeX XMLCite \textit{É. Fouvry} and \textit{I. E. Shparlinski}, Publ. Math. Debr. 79, No. 3--4, 423--432 (2011; Zbl 1249.11095) Full Text: DOI
Fouvry, Étienne; Shparlinski, Igor E. On a ternary quadratic form over primes. (English) Zbl 1243.11093 Acta Arith. 150, No. 3, 285-314 (2011). Reviewer: Angel V. Kumchev (Towson) MSC: 11N25 11L20 11N35 PDFBibTeX XMLCite \textit{É. Fouvry} and \textit{I. E. Shparlinski}, Acta Arith. 150, No. 3, 285--314 (2011; Zbl 1243.11093) Full Text: DOI
Shparlinski, Igor E. Bounds of multiplicative character sums with Fermat quotients of primes. (English) Zbl 1221.11004 Bull. Aust. Math. Soc. 83, No. 3, 456-462 (2011). Reviewer: Huaning Liu (Shaanxi) MSC: 11A07 11L40 11N25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Bull. Aust. Math. Soc. 83, No. 3, 456--462 (2011; Zbl 1221.11004) Full Text: DOI
Bourgain, Jean; Konyagin, Sergei; Shparlinski, Igor Distribution on elements of cosets of small subgroups and applications. arXiv:1103.0567 Preprint, arXiv:1103.0567 [math.NT] (2011). MSC: 11A15 11L07 11N25 BibTeX Cite \textit{J. Bourgain} et al., ``Distribution on elements of cosets of small subgroups and applications'', Preprint, arXiv:1103.0567 [math.NT] (2011) Full Text: arXiv OA License
Loiperdinger, Stefanie S.; Shparlinski, Igor E. On the distribution of the Euler function of shifted smooth numbers. (English) Zbl 1251.11064 Colloq. Math. 120, No. 1, 139-148 (2010). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11N37 PDFBibTeX XMLCite \textit{S. S. Loiperdinger} and \textit{I. E. Shparlinski}, Colloq. Math. 120, No. 1, 139--148 (2010; Zbl 1251.11064) Full Text: DOI arXiv
Pomerance, Carl; Shparlinski, Igor E. Rank statistics for a family of elliptic curves over a function field. (English) Zbl 1200.14060 Pure Appl. Math. Q. 6, No. 1, 21-40 (2010). Reviewer: Vasyl I. Andriychuk (Lviv) MSC: 14H52 14H05 11N25 11R37 PDFBibTeX XMLCite \textit{C. Pomerance} and \textit{I. E. Shparlinski}, Pure Appl. Math. Q. 6, No. 1, 21--40 (2010; Zbl 1200.14060) Full Text: DOI arXiv
Balasuriya, Sanka; Shparlinski, Igor E.; Sutantyo, Daniel Multiplicative character sums with the Euler function. (English) Zbl 1240.11095 Stud. Sci. Math. Hung. 46, No. 2, 223-229 (2009). Reviewer: John H. Loxton (Greenwich, New South Wales) MSC: 11L40 11N25 PDFBibTeX XMLCite \textit{S. Balasuriya} et al., Stud. Sci. Math. Hung. 46, No. 2, 223--229 (2009; Zbl 1240.11095) Full Text: DOI
Friedlander, John B.; Shparlinski, Igor E. On the density of some special primes. (English) Zbl 1246.11154 J. Math. Cryptol. 3, No. 3, 265-271 (2009). Reviewer: Jan-Christoph Schlage-Puchta (Gent) MSC: 11N05 11N25 11A07 PDFBibTeX XMLCite \textit{J. B. Friedlander} and \textit{I. E. Shparlinski}, J. Math. Cryptol. 3, No. 3, 265--271 (2009; Zbl 1246.11154) Full Text: DOI
Luca, Florian; Pomerance, Carl; Shparlinski, Igor On Giuga numbers. (English) Zbl 1231.11115 Int. J. Mod. Math. 4, No. 1, 13-18 (2009). MSC: 11N25 PDFBibTeX XMLCite \textit{F. Luca} et al., Int. J. Mod. Math. 4, No. 1, 13--18 (2009; Zbl 1231.11115)
Ford, Kevin; Luca, Florian; Shparlinski, Igor E. On the largest prime factor of the Mersenne numbers. (English) Zbl 1178.11061 Bull. Aust. Math. Soc. 79, No. 3, 455-463 (2009). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11N36 PDFBibTeX XMLCite \textit{K. Ford} et al., Bull. Aust. Math. Soc. 79, No. 3, 455--463 (2009; Zbl 1178.11061) Full Text: DOI arXiv
Graham, Sidney W.; Shparlinski, Igor E. On RSA moduli with almost half of the bits prescribed. (English) Zbl 1172.11046 Discrete Appl. Math. 156, No. 16, 3150-3154 (2008). Reviewer: Sergey Stepanov (Moskva) MSC: 11T71 11L40 94A60 11N25 11Y16 PDFBibTeX XMLCite \textit{S. W. Graham} and \textit{I. E. Shparlinski}, Discrete Appl. Math. 156, No. 16, 3150--3154 (2008; Zbl 1172.11046) Full Text: DOI arXiv
Friedlander, John B.; Kurlberg, Pär; Shparlinski, Igor E. Products in residue classes. (English) Zbl 1182.11046 Math. Res. Lett. 15, No. 5-6, 1133-1147 (2008). Reviewer: Roger Heath-Brown (Oxford) MSC: 11N69 11N25 PDFBibTeX XMLCite \textit{J. B. Friedlander} et al., Math. Res. Lett. 15, No. 5--6, 1133--1147 (2008; Zbl 1182.11046) Full Text: DOI arXiv
Khan, Mizan R.; Shparlinski, Igor E.; Yankov, Christian L. On the convex closure of the graph of modular inversions. (English) Zbl 1234.11005 Exp. Math. 17, No. 1, 91-104 (2008). MSC: 11A07 11H06 11K38 11N25 PDFBibTeX XMLCite \textit{M. R. Khan} et al., Exp. Math. 17, No. 1, 91--104 (2008; Zbl 1234.11005) Full Text: DOI arXiv Euclid
Shparlinski, Igor E. Approximation by several rationals. (English) Zbl 1157.11029 Bull. Aust. Math. Soc. 77, No. 2, 325-329 (2008). Reviewer: Tatiana Hessami Pilehrood (Shahrekord) MSC: 11J04 11N25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Bull. Aust. Math. Soc. 77, No. 2, 325--329 (2008; Zbl 1157.11029) Full Text: DOI arXiv
Shparlinski, Igor E. On the Euler function on differences between the coordinates of points on modular hyperbolas. (English) Zbl 1144.11004 Bull. Pol. Acad. Sci., Math. 56, No. 1, 1-7 (2008). Reviewer: Pieter Moree (Bonn) MSC: 11A07 11K38 11N25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Bull. Pol. Acad. Sci., Math. 56, No. 1, 1--7 (2008; Zbl 1144.11004) Full Text: DOI
Luca, Florian; Shparlinski, Igor E. On the values of the divisor function. (English) Zbl 1241.11115 Monatsh. Math. 154, No. 1, 59-69 (2008). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N25 11N60 PDFBibTeX XMLCite \textit{F. Luca} and \textit{I. E. Shparlinski}, Monatsh. Math. 154, No. 1, 59--69 (2008; Zbl 1241.11115) Full Text: DOI
Shparlinski, Igor E.; Winterhof, Arne On the number of distances between the coordinates of points on modular hyperbolas. (English) Zbl 1137.11063 J. Number Theory 128, No. 5, 1224-1230 (2008). Reviewer: Pieter Moree (Bonn) MSC: 11N25 11A07 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{A. Winterhof}, J. Number Theory 128, No. 5, 1224--1230 (2008; Zbl 1137.11063) Full Text: DOI
Shparlinski, Igor E. Infinite Hilbert class field towers over cyclotomic fields. (English) Zbl 1186.11068 Glasg. Math. J. 50, No. 1, 27-32 (2008). Reviewer: Teruo Takeuchi (Niigata) MSC: 11R37 11R18 11N25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Glasg. Math. J. 50, No. 1, 27--32 (2008; Zbl 1186.11068) Full Text: DOI
Becheanu, Mircea; Luca, Florian; Shparlinski, Igor E. On the sums of complementary divisors. (English) Zbl 1234.11125 Int. J. Number Theory 3, No. 4, 635-648 (2007). Reviewer: Olaf Ninnemann (Berlin) MSC: 11N25 11N37 11L40 PDFBibTeX XMLCite \textit{M. Becheanu} et al., Int. J. Number Theory 3, No. 4, 635--648 (2007; Zbl 1234.11125) Full Text: DOI
Banks, William D.; Luca, Florian; Shparlinski, Igor E. Estimates for Wieferich numbers. (English) Zbl 1138.11002 Ramanujan J. 14, No. 3, 361-378 (2007). Reviewer: Pieter Moree (Bonn) MSC: 11A07 11N25 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Ramanujan J. 14, No. 3, 361--378 (2007; Zbl 1138.11002) Full Text: DOI
Banks, William D.; Luca, Florian; Shparlinski, Igor E. On rough and smooth neighbors. (English) Zbl 1134.11035 Rev. Mat. Complut. 20, No. 1, 109-118 (2007). Reviewer: Pieter Moree (Bonn) MSC: 11N25 11N64 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Rev. Mat. Complut. 20, No. 1, 109--118 (2007; Zbl 1134.11035) Full Text: DOI EuDML
Shparlinski, Igor E.; Sutantyo, Daniel On the set of the largest prime divisors. (English) Zbl 1136.11058 Publ. Math. Debr. 71, No. 1-2, 95-100 (2007). Reviewer: Florian Luca (Morelia) MSC: 11N25 11N64 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{D. Sutantyo}, Publ. Math. Debr. 71, No. 1--2, 95--100 (2007; Zbl 1136.11058)
Luca, Florian; Shparlinski, Igor E. Pseudoprimes in certain linear recurrences. (English) Zbl 1130.11053 Albanian J. Math. 1, No. 3, 125-131 (2007). Reviewer: Pieter Moree (Bonn) MSC: 11N25 11N37 11A07 PDFBibTeX XMLCite \textit{F. Luca} and \textit{I. E. Shparlinski}, Albanian J. Math. 1, No. 3, 125--131 (2007; Zbl 1130.11053) Full Text: Link
Shparlinski, Igor E. Character sums over shifted smooth numbers. (English) Zbl 1166.11028 Proc. Am. Math. Soc. 135, No. 9, 2699-2705 (2007). Reviewer: Chunlei Liu (Shanghai) MSC: 11L40 11N25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 135, No. 9, 2699--2705 (2007; Zbl 1166.11028) Full Text: DOI
Banks, William D.; Shparlinski, Igor E. On values taken by the largest prime factor of shifted primes. (English) Zbl 1139.11038 J. Aust. Math. Soc. 82, No. 1, 133-147 (2007). Reviewer: Angel V. Kumchev (Towson) MSC: 11N25 11N64 PDFBibTeX XMLCite \textit{W. D. Banks} and \textit{I. E. Shparlinski}, J. Aust. Math. Soc. 82, No. 1, 133--147 (2007; Zbl 1139.11038) Full Text: DOI Link
Luca, Florian; Shparlinski, Igor E. Pseudoprime Cullen and Woodall numbers. (English) Zbl 1153.11048 Colloq. Math. 107, No. 1, 35-43 (2007). MSC: 11N25 11A07 11B83 PDFBibTeX XMLCite \textit{F. Luca} and \textit{I. E. Shparlinski}, Colloq. Math. 107, No. 1, 35--43 (2007; Zbl 1153.11048) Full Text: DOI
Banks, William D.; Friedlander, John B.; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E. Coincidences in the values of the Euler and Carmichael functions. (English) Zbl 1195.11128 Acta Arith. 122, No. 3, 207-234 (2006). MSC: 11N37 11N25 11N64 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Acta Arith. 122, No. 3, 207--234 (2006; Zbl 1195.11128) Full Text: DOI
Shparlinski, Igor E. On RSA moduli with prescribed bit patterns. (English) Zbl 1172.11047 Des. Codes Cryptography 39, No. 1, 113-122 (2006). MSC: 11T71 11N25 11T23 11Y16 94A60 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Des. Codes Cryptography 39, No. 1, 113--122 (2006; Zbl 1172.11047) Full Text: DOI
Banks, William D.; Luca, Florian; Shparlinski, Igor E. On certain sums related to multiple divisibility by the largest prime factor. (English) Zbl 1138.11340 Ann. Sci. Math. Qué. 29, No. 2, 131-145 (2005). MSC: 11N37 11N25 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Ann. Sci. Math. Qué. 29, No. 2, 131--145 (2005; Zbl 1138.11340) Full Text: Link
Banks, William D.; Harman, Glyn; Shparlinski, Igor E. Distributional properties of the largest prime factor. (English) Zbl 1090.11059 Mich. Math. J. 53, No. 3, 665-681 (2005). Reviewer: Aleksandar Ivić (Beograd) MSC: 11N37 11N13 11N25 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Mich. Math. J. 53, No. 3, 665--681 (2005; Zbl 1090.11059) Full Text: DOI Euclid
Levieil, Eric; Luca, Florian; Shparlinski, Igor E. Prime divisors of some shifted products. (English) Zbl 1089.11022 Int. J. Math. Math. Sci. 2005, No. 19, 3057-3073 (2005). Reviewer: Manouchehr Misaghian (Charlotte) MSC: 11D75 11B39 11N25 11A51 PDFBibTeX XMLCite \textit{E. Levieil} et al., Int. J. Math. Math. Sci. 2005, No. 19, 3057--3073 (2005; Zbl 1089.11022) Full Text: DOI EuDML
Luca, Florian; Shparlinski, Igor E. Prime divisors of shifted factorials. (English) Zbl 1098.11047 Bull. Lond. Math. Soc. 37, No. 6, 809-817 (2005). Reviewer: László Tóth (Pécs) MSC: 11N25 11D75 11J25 11N69 11J86 PDFBibTeX XMLCite \textit{F. Luca} and \textit{I. E. Shparlinski}, Bull. Lond. Math. Soc. 37, No. 6, 809--817 (2005; Zbl 1098.11047) Full Text: DOI
Banks, William D.; Ford, Kevin; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E. Values of the Euler function in various sequences. (English) Zbl 1197.11125 Monatsh. Math. 146, No. 1, 1-19 (2005). MSC: 11N25 11N64 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Monatsh. Math. 146, No. 1, 1--19 (2005; Zbl 1197.11125) Full Text: DOI Link
Ford, Kevin; Khan, Mizan R.; Shparlinski, Igor E.; Yankov, Christian L. On the maximal difference between an element and its inverse in residue rings. (English) Zbl 1131.11005 Proc. Am. Math. Soc. 133, No. 12, 3463-3468 (2005). MSC: 11A07 11N25 PDFBibTeX XMLCite \textit{K. Ford} et al., Proc. Am. Math. Soc. 133, No. 12, 3463--3468 (2005; Zbl 1131.11005) Full Text: DOI
De Koninck, Jean-Marie; Luca, Florian; Shparlinski, Igor E. Powerful numbers in short intervals. (English) Zbl 1173.11346 Bull. Aust. Math. Soc. 71, No. 1, 11-16 (2005). MSC: 11N25 11J13 11N36 PDFBibTeX XMLCite \textit{J.-M. De Koninck} et al., Bull. Aust. Math. Soc. 71, No. 1, 11--16 (2005; Zbl 1173.11346) Full Text: DOI
Banks, William D.; Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. Multiplicative structure of values of the Euler function. (English) Zbl 1099.11055 van der Poorten, Alf (ed.) et al., High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams. Selected papers from the international conference on number theory, Banff, AB, Canada, May 24–30, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3353-7/hbk). Fields Institute Communications 41, 29-47 (2004). Reviewer: Jürgen Spilker (Freiburg i. Br.) MSC: 11N60 11N25 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Fields Inst. Commun. 41, 29--47 (2004; Zbl 1099.11055)
Banks, William D.; Harcharras, Asma; Shparlinski, Igor E. Smooth values of shifted primes in arithmetic progressions. (English) Zbl 1068.11061 Mich. Math. J. 52, No. 3, 603-618 (2004). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11N13 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Mich. Math. J. 52, No. 3, 603--618 (2004; Zbl 1068.11061) Full Text: DOI
Luca, Florian; Mireles, David Jose; Shparlinski, Igor E. MOV attack in various subgroups on elliptic curves. (English) Zbl 1072.11094 Ill. J. Math. 48, No. 3, 1041-1052 (2004). Reviewer: Tanja Lange (Lyngby) MSC: 11T71 11N25 14H52 PDFBibTeX XMLCite \textit{F. Luca} et al., Ill. J. Math. 48, No. 3, 1041--1052 (2004; Zbl 1072.11094)
Shparlinski, Igor E. Distribution of exponential functions with squarefull exponent in residue rings. (English) Zbl 1108.11070 Indag. Math., New Ser. 15, No. 2, 283-289 (2004). Reviewer: Mongi Naimi (Tunis) MSC: 11N37 11N25 11T23 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Indag. Math., New Ser. 15, No. 2, 283--289 (2004; Zbl 1108.11070) Full Text: DOI
Pappalardi, Francesco; Saidak, Filip; Shparlinski, Igor E. Square-free values of the Carmichael function. (English) Zbl 1042.11058 J. Number Theory 103, No. 1, 122-131 (2003). Reviewer: Florian Luca (Morelia) MSC: 11N25 11N05 11N37 PDFBibTeX XMLCite \textit{F. Pappalardi} et al., J. Number Theory 103, No. 1, 122--131 (2003; Zbl 1042.11058) Full Text: DOI
Pomerance, Carl; Shparlinski, Igor E. Smooth orders and cryptographic applications. (English) Zbl 1058.11059 Fieker, Claus (ed.) et al., Algorithmic number theory. 5th international symposium, ANTS-V, Sydney, Australia, July 7–12, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43863-7). Lect. Notes Comput. Sci. 2369, 338-348 (2002). MSC: 11N25 94A60 PDFBibTeX XMLCite \textit{C. Pomerance} and \textit{I. E. Shparlinski}, Lect. Notes Comput. Sci. 2369, 338--348 (2002; Zbl 1058.11059) Full Text: Link
Bernasconi, Anna; Damm, Carsten; Shparlinski, Igor The average sensitivity of square-freeness. (English) Zbl 1045.11513 Comput. Complexity 9, No. 1, 39-51 (2000). MSC: 11N25 11Z05 68Q25 94C10 PDFBibTeX XMLCite \textit{A. Bernasconi} et al., Comput. Complexity 9, No. 1, 39--51 (2000; Zbl 1045.11513) Full Text: DOI