## Silverman, Joseph Hillel

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 Author ID: silverman.joseph-hillel Published as: Silverman, Joseph H.; Silverman, J. H.; Silverman, Joseph Homepage: http://www.math.brown.edu/johsilve/ External Links: MGP · ORCID · Wikidata · MathOverflow · dblp · GND · IdRef
 Documents Indexed: 170 Publications since 1978, including 12 Books 5 Contributions as Editor · 1 Further Contribution Co-Authors: 78 Co-Authors with 79 Joint Publications 1,635 Co-Co-Authors
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### Co-Authors

 96 single-authored 15 Hoffstein, Jeffrey 9 Kawaguchi, Shu 9 Pipher, Jill Catherine 9 Whyte, William 5 Ingram, Patrick 4 Hindry, Marc 4 Rosen, Michael I. 4 Voloch, José Felipe 3 Call, Gregory S. 3 Cornell, Gary 3 Howgrave-Graham, Nick A. 3 Manes, Michelle 3 Schanck, John M. 3 Shparlinski, Igor E. 3 Stange, Katherine E. 3 Zhang, Zhenfei 2 Doyle, John R. 2 Hsia, Liang-Chung 2 Jacobson, Michael John jun. 2 Jones, Rafe 2 Morton, Patrick 2 Murty, Maruti Ram 2 Ostafe, Alina 2 Stevens, Glenn 2 Tate, John Torrence jun. 1 Acquista, Karen 1 Ahmadi, Omran 1 Bailey, Daniel V. 1 Baker, Matthew H. 1 Ball, L. Simeon 1 Benedetto, Robert L. 1 Bérczes, Attila 1 Bernstein, Daniel Julius 1 Blache, Régis 1 Blake, Ian F. 1 Blokhuis, Aart 1 Bremner, Andrew 1 Bridy, Andrew 1 Brumer, Armand 1 Buhler, Joe P. 1 Carlet, Claude 1 Castro, Francis Noel 1 Chand Gupta, Kishan 1 Charpin, Pascale 1 Cioabă, Sebastian M. 1 Clausen, Dustin 1 Coates, John H. 1 Coffin, Daniel 1 Cohen, Stephen D. 1 Colbourn, Charles J. 1 Coulter, Robert S. 1 de Smit, Bart 1 Ding, Jintai 1 Dinitz, Jeffrey H. 1 Doche, Christophe 1 Doröz, Yarkın 1 Dumas, Jean-Guillaume 1 Ebert, Gary Lee 1 Effinger, Gove W. 1 Elbirt, Adam J. 1 Enge, Andreas 1 Evans, Ronald J. 1 Evertse, Jan-Hendrik 1 Fan, Haining 1 Fitzgerald, Robert W. 1 Fried, Michael David 1 Fu, Lei 1 Gao, Shuhong 1 Garaev, Moubariz Z. 1 Garcia, Arnaldo 1 Giesbrecht, Mark W. 1 Gong, Guang 1 Goss, David Mark 1 Gow, Roderick 1 Gross, Benedict Hyman 1 Hachenberger, Dirk 1 Hardy, Godfrey Harold 1 Harris, Joseph Daniel 1 Hasan, M. Anwar 1 Heath-Brown, Roger 1 Helleseth, Tor 1 Hinkelmann, Franziska 1 Hirschfeld, James William Peter 1 Hou, Xiang-Dong 1 Huffman, W. Cary 1 Jedwab, Jonathan 1 Joyce, Michael 1 Jungnickel, Dieter 1 Juul, Jamie 1 Kaltofen, Erich L. 1 Kholosha, Alexander 1 Koblitz, Neal I. 1 Kyuregyan, Melsik K. 1 Lange, Tanja 1 Laubenbacher, Reinhard C. 1 Lecerf, Grégoire 1 Lee, Chong Gyu 1 Lenstra, Hendrik W. jun. 1 Levy, Alon 1 Liao, Qunying ...and 63 more Co-Authors
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### Serials

 11 Journal of Number Theory 8 Journal für die Reine und Angewandte Mathematik 7 Inventiones Mathematicae 5 Mathematics of Computation 5 Acta Arithmetica 5 Duke Mathematical Journal 5 Graduate Texts in Mathematics 4 Compositio Mathematica 4 Proceedings of the American Mathematical Society 4 Designs, Codes and Cryptography 4 Undergraduate Texts in Mathematics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Mathematische Annalen 3 Pacific Journal of Mathematics 3 Transactions of the American Mathematical Society 3 Journal de Théorie des Nombres de Bordeaux 3 The New York Journal of Mathematics 3 Mathematical Research Letters 2 American Mathematical Monthly 2 American Journal of Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Manuscripta Mathematica 2 Mathematische Zeitschrift 2 Proceedings of the London Mathematical Society. Third Series 2 Ergodic Theory and Dynamical Systems 2 Journal of the Ramanujan Mathematical Society 2 IMRN. International Mathematics Research Notices 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Experimental Mathematics 2 Journal of Algebraic Geometry 2 Pure and Applied Mathematics Quarterly 1 Discrete Applied Mathematics 1 Rocky Mountain Journal of Mathematics 1 Mathematics Magazine 1 Illinois Journal of Mathematics 1 Journal of Algebra 1 Mathematika 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Theoretical Computer Science 1 International Journal of Mathematics 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Finite Fields and their Applications 1 Documenta Mathematica 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Journal of the Australian Mathematical Society 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 CRM Monograph Series 1 Lecture Notes in Computer Science 1 Journal of Mathematical Cryptology 1 Advances in Mathematics of Communications 1 Pure and Applied Undergraduate Texts 1 Discrete Mathematics and its Applications
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### Fields

 119 Number theory (11-XX) 106 Algebraic geometry (14-XX) 39 Dynamical systems and ergodic theory (37-XX) 30 Information and communication theory, circuits (94-XX) 5 General and overarching topics; collections (00-XX) 4 Field theory and polynomials (12-XX) 3 History and biography (01-XX) 3 Computer science (68-XX) 2 Group theory and generalizations (20-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Numerical analysis (65-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

147 Publications have been cited 4,363 times in 2,638 Documents Cited by Year
The arithmetic of elliptic curves. Zbl 0585.14026
Silverman, Joseph H.
1986
The arithmetic of elliptic curves. 2nd ed. Zbl 1194.11005
Silverman, Joseph H.
2009
Advanced topics in the arithmetic of elliptic curves. Zbl 0911.14015
Silverman, Joseph H.
1994
An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001
Hardy, G. H.; Wright, E. M.
2008
Diophantine geometry. An introduction. Zbl 0948.11023
Hindry, Marc; Silverman, Joseph H.
2000
The arithmetic of dynamical systems. Zbl 1130.37001
Silverman, Joseph H.
2007
Handbook of finite fields. Zbl 1319.11001
2013
Rational points on elliptic curves. Zbl 0752.14034
Silverman, Joseph H.; Tate, John
1992
NTRU: A ring-based public key cryptosystem. Zbl 1067.94538
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
1998
Canonical heights on varieties with morphisms. Zbl 0826.14015
Call, Gregory S.; Silverman, Joseph H.
1993
Wieferich’s criterion and the abc-conjecture. Zbl 0654.10019
Silverman, Joseph H.
1988
Heights and the specialization map for families of abelian varieties. Zbl 0505.14035
Silverman, Joseph H.
1983
Rational periodic points of rational functions. Zbl 0819.11045
Morton, Patrick; Silverman, Joseph H.
1994
The canonical height and integral points on elliptic curves. Zbl 0657.14018
Hindry, M.; Silverman, J. H.
1988
The difference between the Weil height and the canonical height on elliptic curves. Zbl 0729.14026
Silverman, Joseph H.
1990
Lower bounds for height functions. Zbl 0579.14035
Silverman, Joseph H.
1984
The space of rational maps on $$\mathbf P^1$$. Zbl 0966.14031
Silverman, Joseph H.
1998
Periodic points, multiplicities, and dynamical units. Zbl 0813.11059
Morton, Patrick; Silverman, Joseph H.
1995
Computig heights on elliptic curves. Zbl 0656.14016
Silverman, Joseph H.
1988
Integer points, diophantine approximation, and iteration of rational maps. Zbl 0811.11052
Silverman, Joseph H.
1993
Arithmetic geometry. (Papers presented at the Conference held from July 30 through August 10, 1984 at the University of Connecticut in Storrs). Zbl 0596.00007
1986
Rational points on K3 surfaces: A new canonical height. Zbl 0754.14023
Silverman, Joseph H.
1991
Lower bound for the canonical height on elliptic curves. Zbl 0475.14033
Silverman, Joseph H.
1981
An introduction to mathematical cryptography. Zbl 1160.94001
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
2008
Bielliptic curves and symmetric products. Zbl 0727.11023
Harris, Joe; Silverman, Joseph H.
1991
Primitive divisors in arithmetic dynamics. Zbl 1242.11012
Ingram, Patrick; Silverman, Joseph H.
2009
Arithmetic distance functions and height functions in diophantine geometry. Zbl 0607.14013
Silverman, Joseph H.
1987
The number of elliptic curves over $$\mathbb{Q}$$ with conductor $$N$$. Zbl 0868.11029
Brumer, Armand; Silverman, Joseph H.
1996
Generalized greatest common divisors, divisibility sequences, and Vojta’s conjecture for blowups. Zbl 1197.11070
Silverman, Joseph H.
2005
NTRUSign: Digital signatures using the NTRU lattice. Zbl 1039.94525
Hoffstein, Jeffrey; Howgrave-Graham, Nick; Pipher, Jill; Silverman, Joseph H.; Whyte, William
2003
On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties. Zbl 1393.37115
Kawaguchi, Shu; Silverman, Joseph H.
2016
Integral points in arithmetic progression on $$y^2= x(x^2-n^2)$$. Zbl 1009.11035
Bremner, A.; Silverman, J. H.; Tzanakis, N.
2000
Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. Zbl 1372.37093
Silverman, Joseph H.
2014
Divisibility of the specialization map for families of elliptic curves. Zbl 0613.14029
Silverman, Joseph H.
1985
Moduli spaces and arithmetic dynamics. Zbl 1247.37004
Silverman, Joseph H.
2012
An inequality relating the regulator and the discriminant of a number field. Zbl 0552.12003
Silverman, Joseph H.
1984
The field of definition for dynamical systems on $$\mathbb{P}^ 1$$. Zbl 0849.11090
Silverman, Joseph H.
1995
Uniform bounds for the number of solutions to $$Y^ n=f(X)$$. Zbl 0611.10009
Evertse, J.-H.; Silverman, J. H.
1986
The S-unit equation over function fields. Zbl 0533.10013
Silverman, Joseph H.
1984
Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties. Zbl 1391.37078
Kawaguchi, Shu; Silverman, Joseph H.
2016
Rational points on elliptic curves. 2nd ed. Zbl 1346.11001
Silverman, Joseph H.; Tate, John T.
2015
On the distribution of integer points on curves of genus zero. Zbl 0979.11037
Silverman, J. H.
2000
The Markoff equation $$X^ 2+Y^ 2+Z^ 2=aXYZ$$ over quadratic imaginary fields. Zbl 0702.11012
Silverman, Joseph H.
1990
Examples of dynamical degree equals arithmetic degree. Zbl 1309.37084
Kawaguchi, Shu; Silverman, Joseph H.
2014
Integer points and the rank of Thue elliptic curves. Zbl 0494.14008
Silverman, Joseph H.
1982
Arithmetic and dynamical degrees on abelian varieties. Zbl 1416.11091
Silverman, Joseph H.
2017
Variation of periods modulo $$p$$ in arithmetic dynamics. Zbl 1153.11028
Silverman, Joseph H.
2008
Geometric and arithmetic properties of the Hénon map. Zbl 0807.58021
Silverman, Joseph H.
1994
A quantitative version of Siegel’s theorem: integral points on elliptic curves and Catalan curves. Zbl 0608.14021
Silverman, Joseph H.
1987
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Paperback ed. Zbl 1051.11500
2000
Integer points on curves of genus 1. Zbl 0487.10015
Silverman, Joseph H.
1983
On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504
Shparlinski, Igor E.; Silverman, Joseph H.
2001
Common divisors of elliptic divisibility sequences over function fields. Zbl 1128.11015
Silverman, Joseph H.
2004
On the rank of an elliptic surface. Zbl 0905.14019
Rosen, Michael; Silverman, Joseph H.
1998
Representations of integers by binary forms and the rank of the Mordell- Weil group. Zbl 0525.14012
Silverman, J. H.
1983
Dynamics of projective morphisms having identical canonical heights. Zbl 1130.11035
Kawaguchi, Shu; Silverman, Joseph H.
2007
Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092
Ingram, Patrick; Silverman, Joseph H.
2012
Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture. Zbl 1297.37046
Silverman, Joseph H.
2013
On the number of rational torsion points on an elliptic curve. (Sur le nombre de points de torsion rationnels sur une courbe elliptique.) Zbl 0993.11028
Hindry, Marc; Silverman, Joseph
1999
Choosing parameters for NTRUEncrypt. Zbl 1383.94022
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei
2017
An upper bound for the conductor of an abelian variety. Zbl 0816.14021
Lockhart, Paul; Rosen, Michael; Silverman, Joseph H.
1993
Heights and elliptic curves. Zbl 0603.14020
Silverman, Joseph H.
1986
The Xedni calculus and the elliptic curve discrete logarithm problem. Zbl 0948.11049
Silverman, Joseph H.
2000
Exceptional units and numbers of small Mahler measure. Zbl 0851.11064
Silverman, Joseph H.
1995
$$p$$-adic properties of division polynomials and elliptic divisibility sequences. Zbl 1066.11024
Silverman, Joseph H.
2005
NSS: an NTRU lattice-based signature scheme. Zbl 0981.94039
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
2001
Nonarchimedean Green functions and dynamics on projective space. Zbl 1161.32009
Kawaguchi, Shu; Silverman, Joseph H.
2009
A lower bound for the canonical height on abelian varieties over abelian extensions. Zbl 1060.11041
Baker, Matthew H.; Silverman, Joseph H.
2004
Analysis of the Xedni calculus attack. Zbl 0948.11048
Jacobson, Michael J.; Koblitz, Neal; Silverman, Joseph H.; Stein, Andreas; Teske, Edlyn
2000
On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024
Rosen, Michael; Silverman, Joseph H.
2007
Current trends and open problems in arithmetic dynamics. Zbl 1468.37001
Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J.
2019
The average rank of an algebraic family of elliptic curves. Zbl 0923.11087
Silverman, Joseph H.
1998
A lower bound for the canonical height on elliptic curves over abelian extensions. Zbl 1053.11052
Silverman, Joseph H.
2004
On Lehmer’s conjecture for elliptic curves. Zbl 0741.14013
Hindry, Marc; Silverman, Joseph H.
1990
On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture. Zbl 1347.37153
Silverman, Joseph H.; Viray, Bianca
2013
Variations on a theme of Romanoff. Zbl 0869.11004
Murty, M. Ram; Rosen, Michael; Silverman, Joseph H.
1996
The impact of decryption failures on the security of NTRU encryption. Zbl 1122.94377
Howgrave-Graham, Nick; Nguyen, Phong Q.; Pointcheval, David; Proos, John; Silverman, Joseph H.; Singer, Ari; Whyte, William
2003
Terms in elliptic divisibility sequences divisible by their indices. Zbl 1225.11079
Silverman, Joseph H.; Stange, Katherine E.
2011
A local-global criterion for dynamics on $${\mathbb P}^1$$. Zbl 1243.37066
Silverman, Joseph H.; Voloch, José Felipe
2009
Computing rational points on rank 1 elliptic curves via $$L$$-series and canonical heights. Zbl 1042.11036
Silverman, Joseph H.
1999
Dimension reduction methods for convolution modular lattices. Zbl 1006.11033
May, Alexander; Silverman, Joseph H.
2001
Amicable pairs and aliquot cycles for elliptic curves. Zbl 1269.11056
Silverman, Joseph H.; Stange, Katherine E.
2011
The rank of elliptic surfaces in unramified abelian towers. Zbl 1105.11016
Silverman, Joseph H.
2004
Rational points on certain families of curves of genus at least 2. Zbl 0642.14006
Silverman, Joseph H.
1987
Small Salem numbers, exceptional units, and Lehmer’s conjecture. Zbl 0883.11045
Silverman, Joseph H.
1996
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Zbl 0878.11004
1997
Computing canonical heights with little (or no) factorization. Zbl 0898.11021
Silverman, Joseph H.
1997
Common divisors of $$a^n-1$$ and $$b^n-1$$ over function fields. Zbl 1120.11045
Silverman, Joseph H.
2004
Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. Zbl 1079.94553
Howgrave-Graham, Nick; Silverman, Joseph H.; Whyte, William
2005
The Neron fiber of Abelian varieties with potential good reduction. Zbl 0497.14016
Silverman, Joseph H.
1983
Taxicabs and sums of two cubes. Zbl 0796.11022
Silverman, Joseph H.
1993
The sign of an elliptic divisibility sequence. Zbl 1148.11013
Silverman, Joseph H.; Stephens, Nelson
2006
$$S$$-integer points on elliptic curves. Zbl 0824.11038
Gross, Robert; Silverman, Joseph
1995
Elliptic curve discrete logarithms and the index calculus. Zbl 0944.11043
Silverman, Joseph H.; Suzuki, Joe
1998
The Catalan equation over function fields. Zbl 0493.10020
Silverman, Joseph H.
1982
Hecke points on modular curves. Zbl 0744.14014
Silverman, Joseph H.
1990
Height estimates for equidimensional dominant rational maps. Zbl 1311.11057
Silverman, Joseph H.
2011
Some arithmetic properties of Weierstrass points: Hyperelliptic curves. Zbl 0758.14023
Silverman, Joseph H.
1990
A bound for the Mordell-Weil rank of an elliptic surface after a cyclic base extension. Zbl 0951.14023
Silverman, Joseph H.
2000
Random small Hamming weight products with applications to cryptography. Zbl 1028.94023
Hoffstein, Jeffrey; Silverman, Joseph H.
2003
Moduli spaces for dynamical systems with portraits. Zbl 1448.37132
Doyle, John R.; Silverman, Joseph H.
2020
Erratum to “On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties”. Zbl 1439.37090
Kawaguchi, Shu; Silverman, Joseph H.
2020
GIT stability of Hénon maps. Zbl 1448.37133
Lee, Chong Gyu; Silverman, Joseph H.
2020
Current trends and open problems in arithmetic dynamics. Zbl 1468.37001
Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J.
2019
A uniform field-of-definition/field-of-moduli bound for dynamical systems on $$\mathbb{P}^N$$. Zbl 1432.37124
Doyle, John R.; Silverman, Joseph H.
2019
A classification of degree $$2$$ semi-stable rational maps $$\mathbb{P}^2\rightarrow\mathbb{P}^2$$ with large finite dynamical automorphism group. Zbl 1432.37123
Manes, Michelle; Silverman, Joseph H.
2019
Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures. Zbl 1396.37097
Silverman, Joseph H.
2018
Degeneration of dynamical degrees in families of maps. Zbl 1404.37123
Silverman, Joseph H.; Call, Gregory S.
2018
Fully homomorphic encryption from the finite field isomorphism problem. Zbl 1385.94032
Doröz, Yarkın; Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.; Sunar, Berk; Whyte, William; Zhang, Zhenfei
2018
Arithmetic and dynamical degrees on abelian varieties. Zbl 1416.11091
Silverman, Joseph H.
2017
Choosing parameters for NTRUEncrypt. Zbl 1383.94022
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei
2017
Finite ramification for preimage fields of post-critically finite morphisms. Zbl 1391.14004
Bridy, Andrew; Ingram, Patrick; Jones, Rafe; Juul, Jamie; Levy, Alon; Manes, Michelle; Rubinstein-Salzedo, Simon; Silverman, Joseph H.
2017
Rational points on, and the arithmetic of, elliptic curves: a tale of two books (and an article). Zbl 1436.11005
Silverman, Joseph H.
2017
On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties. Zbl 1393.37115
Kawaguchi, Shu; Silverman, Joseph H.
2016
Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties. Zbl 1391.37078
Kawaguchi, Shu; Silverman, Joseph H.
2016
Rational points on elliptic curves. 2nd ed. Zbl 1346.11001
Silverman, Joseph H.; Tate, John T.
2015
Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. Zbl 1372.37093
Silverman, Joseph H.
2014
Examples of dynamical degree equals arithmetic degree. Zbl 1309.37084
Kawaguchi, Shu; Silverman, Joseph H.
2014
Transcript secure signatures based on modular lattices. Zbl 1380.94099
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William
2014
An introduction to mathematical cryptography. 2nd ed. Zbl 1297.94001
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
2014
Practical signatures from the partial Fourier recovery problem. Zbl 1356.94060
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William
2014
Handbook of finite fields. Zbl 1319.11001
2013
Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture. Zbl 1297.37046
Silverman, Joseph H.
2013
On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture. Zbl 1347.37153
Silverman, Joseph H.; Viray, Bianca
2013
What is …the $$p$$-adic Mandelbrot set? Zbl 1322.28001
Silverman, Joseph H.
2013
Moduli spaces and arithmetic dynamics. Zbl 1247.37004
Silverman, Joseph H.
2012
Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092
Ingram, Patrick; Silverman, Joseph H.
2012
Algebraic divisibility sequences over function fields. Zbl 1251.11008
Ingram, Patrick; Mahé, Valéry; Silverman, Joseph H.; Stange, Katherine E.; Streng, Marco
2012
Elliptic Carmichael numbers and elliptic Korselt criteria. Zbl 1304.11047
Silverman, Joseph H.
2012
An algebraic approach to certain cases of Thurston rigidity. Zbl 1291.37072
Silverman, Joseph H.
2012
Terms in elliptic divisibility sequences divisible by their indices. Zbl 1225.11079
Silverman, Joseph H.; Stange, Katherine E.
2011
Amicable pairs and aliquot cycles for elliptic curves. Zbl 1269.11056
Silverman, Joseph H.; Stange, Katherine E.
2011
Height estimates for equidimensional dominant rational maps. Zbl 1311.11057
Silverman, Joseph H.
2011
A quantitative estimate for quasiintegral points in orbits. Zbl 1272.37039
Hsia, Liang-Chung; Silverman, Joseph H.
2011
Lang’s height conjecture and Szpiro’s conjecture. Zbl 1304.11046
Silverman, Joseph H.
2010
The arithmetic of elliptic curves. 2nd ed. Zbl 1194.11005
Silverman, Joseph H.
2009
Primitive divisors in arithmetic dynamics. Zbl 1242.11012
Ingram, Patrick; Silverman, Joseph H.
2009
Nonarchimedean Green functions and dynamics on projective space. Zbl 1161.32009
Kawaguchi, Shu; Silverman, Joseph H.
2009
A local-global criterion for dynamics on $${\mathbb P}^1$$. Zbl 1243.37066
Silverman, Joseph H.; Voloch, José Felipe
2009
On a dynamical Brauer-Manin obstruction. Zbl 1196.37131
Hsia, Liang-Chung; Silverman, Joseph
2009
Canonical heights and the arithmetic complexity of morphisms on projective space. Zbl 1221.11152
Kawaguchi, Shu; Silverman, Joseph H.
2009
Lifting and elliptic curve discrete logarithms. Zbl 1256.94065
Silverman, Joseph H.
2009
An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001
Hardy, G. H.; Wright, E. M.
2008
An introduction to mathematical cryptography. Zbl 1160.94001
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
2008
Variation of periods modulo $$p$$ in arithmetic dynamics. Zbl 1153.11028
Silverman, Joseph H.
2008
The arithmetic of dynamical systems. Zbl 1130.37001
Silverman, Joseph H.
2007
Dynamics of projective morphisms having identical canonical heights. Zbl 1130.11035
Kawaguchi, Shu; Silverman, Joseph H.
2007
On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024
Rosen, Michael; Silverman, Joseph H.
2007
The sign of an elliptic divisibility sequence. Zbl 1148.11013
Silverman, Joseph H.; Stephens, Nelson
2006
Height bounds and preperiodic points for families of jointly regular affine maps. Zbl 1154.11328
Silverman, Joseph H.
2006
Timing attacks on NTRUEncrypt via variation in the number of hash calls. Zbl 1177.94174
Silverman, Joseph H.; Whyte, William
2006
Generalized greatest common divisors, divisibility sequences, and Vojta’s conjecture for blowups. Zbl 1197.11070
Silverman, Joseph H.
2005
$$p$$-adic properties of division polynomials and elliptic divisibility sequences. Zbl 1066.11024
Silverman, Joseph H.
2005
Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. Zbl 1079.94553
Howgrave-Graham, Nick; Silverman, Joseph H.; Whyte, William
2005
An algebraic approach to NTRU ($$q = 2^{n}$$) via Witt vectors and overdetermined systems of nonlinear equations. Zbl 1116.94333
Silverman, J. H.; Smart, N. P.; Vercauteren, F.
2005
Common divisors of elliptic divisibility sequences over function fields. Zbl 1128.11015
Silverman, Joseph H.
2004
A lower bound for the canonical height on abelian varieties over abelian extensions. Zbl 1060.11041
Baker, Matthew H.; Silverman, Joseph H.
2004
A lower bound for the canonical height on elliptic curves over abelian extensions. Zbl 1053.11052
Silverman, Joseph H.
2004
The rank of elliptic surfaces in unramified abelian towers. Zbl 1105.11016
Silverman, Joseph H.
2004
Common divisors of $$a^n-1$$ and $$b^n-1$$ over function fields. Zbl 1120.11045
Silverman, Joseph H.
2004
NTRUSign: Digital signatures using the NTRU lattice. Zbl 1039.94525
Hoffstein, Jeffrey; Howgrave-Graham, Nick; Pipher, Jill; Silverman, Joseph H.; Whyte, William
2003
The impact of decryption failures on the security of NTRU encryption. Zbl 1122.94377
Howgrave-Graham, Nick; Nguyen, Phong Q.; Pointcheval, David; Proos, John; Silverman, Joseph H.; Singer, Ari; Whyte, William
2003
Random small Hamming weight products with applications to cryptography. Zbl 1028.94023
Hoffstein, Jeffrey; Silverman, Joseph H.
2003
On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504
Shparlinski, Igor E.; Silverman, Joseph H.
2001
NSS: an NTRU lattice-based signature scheme. Zbl 0981.94039
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
2001
Dimension reduction methods for convolution modular lattices. Zbl 1006.11033
May, Alexander; Silverman, Joseph H.
2001
Optimizations for NTRU. Zbl 0987.94027
Hoffstein, Jeffrey; Silverman, Joseph
2001
Polynomial rings and efficient public key authentication. II. Zbl 1002.94535
Hoffstein, Jeffrey; Silverman, Joseph H.
2001
NTRU in constrained devices. Zbl 1012.94548
Bailey, Daniel V.; Coffin, Daniel; Elbirt, Adam; Silverman, Joseph H.; Woodbury, Adam D.
2001
Cryptography and lattices. 1st international conference, CaLC 2001, Providence, RI, USA, March 29–30, 2001. Revised papers. Zbl 0971.00060
2001
Diophantine geometry. An introduction. Zbl 0948.11023
Hindry, Marc; Silverman, Joseph H.
2000
Integral points in arithmetic progression on $$y^2= x(x^2-n^2)$$. Zbl 1009.11035
Bremner, A.; Silverman, J. H.; Tzanakis, N.
2000
On the distribution of integer points on curves of genus zero. Zbl 0979.11037
Silverman, J. H.
2000
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Paperback ed. Zbl 1051.11500
2000
The Xedni calculus and the elliptic curve discrete logarithm problem. Zbl 0948.11049
Silverman, Joseph H.
2000
Analysis of the Xedni calculus attack. Zbl 0948.11048
Jacobson, Michael J.; Koblitz, Neal; Silverman, Joseph H.; Stein, Andreas; Teske, Edlyn
2000
A bound for the Mordell-Weil rank of an elliptic surface after a cyclic base extension. Zbl 0951.14023
Silverman, Joseph H.
2000
On the number of rational torsion points on an elliptic curve. (Sur le nombre de points de torsion rationnels sur une courbe elliptique.) Zbl 0993.11028
Hindry, Marc; Silverman, Joseph
1999
Computing rational points on rank 1 elliptic curves via $$L$$-series and canonical heights. Zbl 1042.11036
Silverman, Joseph H.
1999
Fast multiplication in finite fields GF$$(2^N)$$. Zbl 0993.11065
Silverman, Joseph H.
1999
Divisibility of the specialization map for twists of abelian varieties. Zbl 0938.11030
Silverman, Joseph H.
1999
NTRU: A ring-based public key cryptosystem. Zbl 1067.94538
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
1998
The space of rational maps on $$\mathbf P^1$$. Zbl 0966.14031
Silverman, Joseph H.
1998
On the rank of an elliptic surface. Zbl 0905.14019
Rosen, Michael; Silverman, Joseph H.
1998
The average rank of an algebraic family of elliptic curves. Zbl 0923.11087
Silverman, Joseph H.
1998
Elliptic curve discrete logarithms and the index calculus. Zbl 0944.11043
Silverman, Joseph H.; Suzuki, Joe
1998
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Zbl 0878.11004
1997
Computing canonical heights with little (or no) factorization. Zbl 0898.11021
Silverman, Joseph H.
1997
A friendly introduction to number theory. Zbl 0973.11003
Silverman, Joseph H.
1997
The number of elliptic curves over $$\mathbb{Q}$$ with conductor $$N$$. Zbl 0868.11029
Brumer, Armand; Silverman, Joseph H.
1996
Variations on a theme of Romanoff. Zbl 0869.11004
Murty, M. Ram; Rosen, Michael; Silverman, Joseph H.
1996
Small Salem numbers, exceptional units, and Lehmer’s conjecture. Zbl 0883.11045
Silverman, Joseph H.
1996
Rational functions with a polynomial iterate. Zbl 0848.11049
Silverman, Joseph H.
1996
Computing the canonical height on K3 surfaces. Zbl 0865.14020
Call, Gregory S.; Silverman, Joseph H.
1996
Periodic points, multiplicities, and dynamical units. Zbl 0813.11059
Morton, Patrick; Silverman, Joseph H.
1995
The field of definition for dynamical systems on $$\mathbb{P}^ 1$$. Zbl 0849.11090
Silverman, Joseph H.
1995
Exceptional units and numbers of small Mahler measure. Zbl 0851.11064
Silverman, Joseph H.
1995
$$S$$-integer points on elliptic curves. Zbl 0824.11038
Gross, Robert; Silverman, Joseph
1995
Counting integer and rational points on varieties. Zbl 0834.11029
Silverman, Joseph H.
1995
Advanced topics in the arithmetic of elliptic curves. Zbl 0911.14015
Silverman, Joseph H.
1994
...and 47 more Documents
all top 5

### Cited by 2,611 Authors

 59 Silverman, Joseph Hillel 39 Shparlinski, Igor E. 25 Ghioca, Dragos 20 Tucker, Thomas John 18 Ingram, Patrick 17 Ostafe, Alina 17 Zannier, Umberto M. 14 Doyle, John R. 14 Levin, Aaron 14 Murty, Maruti Ram 13 Hindes, Wade 13 Kraus, Alain 12 Clark, Peter Louis 12 González-Jiménez, Enrique 12 Lozano-Robledo, Álvaro 12 Sutherland, Andrew V. 11 Benedetto, Robert L. 11 Everest, Graham Robert 11 Hutz, Benjamin 11 Masser, David William 11 Morton, Patrick 11 Poonen, Bjorn 11 Poulakis, Dimitrios 11 Siksek, Samir 11 Silverberg, Alice 11 Stoll, Michael 10 Dujella, Andrej 10 Fisher, Tom A. 10 Hsia, Liang-Chung 10 Kihara, Shoichi 10 Koo, Jakyung 10 Sha, Min 10 Top, Jaap 10 Ulas, Maciej 10 Zhang, Yong 9 Akbary, Amir 9 Bridy, Andrew 9 Daniels, Harris B. 9 Flynn, Eugene Victor 9 Freitas, Nuno 9 Ono, Ken 9 Rubin, Karl Cooper 9 Voloch, José Felipe 9 Zargar, Arman Shamsi 8 Baragar, Arthur 8 Byeon, Dongho 8 Canci, Jung Kyu 8 Choudhry, Ajai 8 Grant, David R. 8 Jeong, Sangtae 8 Jones, Rafe 8 Kawaguchi, Shu 8 Manes, Michelle 8 Mazur, Barry 8 Mukhamedov, Farruh Maksutovich 8 Müller, Jan Steffen 8 Najman, Filip 8 Nguyen, Khoa Dang 8 Petsche, Clayton 8 Rouse, Jeremy A. 8 Schoen, Chad 8 Tornero, José María 7 Bars Cortina, Francesc 7 Bremner, Andrew 7 Buium, Alexandru 7 Cojocaru, Alina Carmen 7 Cremona, John E. 7 Dąbrowski, Andrzej Bogdan 7 DeMarco, Laura Grace 7 Fan, Shilei 7 Fujita, Yasutsugu Fujita 7 Galbraith, Steven D. 7 Liao, Lingmin 7 Matsuzawa, Yohsuke 7 Moody, Dustin 7 Nikolaev, Igor Vasilievich 7 Okuyama, Yûsuke 7 Pacheco, Amílcar 7 Sadek, Mohammad 7 Shin, Dong Hwa 7 Stewart, Cameron L. 7 Szpiro, Lucien 7 Wang, Julie Tzu-Yueh 7 Wong, Siman 7 Yasufuku, Yu 7 Zarkhin, Yuriĭ Gennad’evich 6 Ahmadi, Omran 6 Bandini, Andrea 6 Bennett, Michael A. 6 Bleher, Frauke M. 6 Castryck, Wouter 6 Dokchitser, Vladimir 6 Faber, Xander 6 Holmes, David 6 Im, Bo-Hae 6 Jeon, Daeyeol 6 Krumm, David 6 Lauter, Kristin Estella 6 Lorenzini, Dino J. 6 Luca, Florian ...and 2,511 more Authors
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### Cited in 304 Serials

 318 Journal of Number Theory 109 Mathematics of Computation 97 Transactions of the American Mathematical Society 83 Journal de Théorie des Nombres de Bordeaux 80 Proceedings of the American Mathematical Society 70 International Journal of Number Theory 60 Mathematische Annalen 53 Compositio Mathematica 51 Journal of Algebra 47 Rocky Mountain Journal of Mathematics 46 Duke Mathematical Journal 44 Proceedings of the Japan Academy. Series A 44 Finite Fields and their Applications 40 Acta Arithmetica 37 Inventiones Mathematicae 36 Mathematische Zeitschrift 30 Advances in Mathematics 30 Research in Number Theory 29 Annales de l’Institut Fourier 28 Designs, Codes and Cryptography 28 Experimental Mathematics 27 Manuscripta Mathematica 27 Monatshefte für Mathematik 26 Journal of Pure and Applied Algebra 26 The Ramanujan Journal 25 LMS Journal of Computation and Mathematics 24 Bulletin of the Australian Mathematical Society 23 Mathematical Proceedings of the Cambridge Philosophical Society 23 Functiones et Approximatio. Commentarii Mathematici 23 Bulletin of the American Mathematical Society. New Series 21 Journal of Mathematical Cryptology 18 Communications in Algebra 18 Israel Journal of Mathematics 18 Archiv der Mathematik 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Journal of Cryptology 15 Journal of the American Mathematical Society 13 Journal für die Reine und Angewandte Mathematik 12 Journal of Symbolic Computation 11 Journal of Mathematical Analysis and Applications 11 Periodica Mathematica Hungarica 11 Ergodic Theory and Dynamical Systems 11 Journal of Algebraic Geometry 11 Algebra & Number Theory 10 Theoretical Computer Science 10 Journal of Discrete Mathematical Sciences & Cryptography 10 Annals of Mathematics. Second Series 9 Tohoku Mathematical Journal. Second Series 9 The New York Journal of Mathematics 9 Journal of the European Mathematical Society (JEMS) 9 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 9 European Journal of Mathematics 8 Communications in Mathematical Physics 8 Discrete Applied Mathematics 8 Proceedings of the London Mathematical Society. Third Series 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 Research in the Mathematical Sciences 7 Bulletin of the London Mathematical Society 7 Glasgow Mathematical Journal 7 Journal of the Mathematical Society of Japan 7 Michigan Mathematical Journal 7 Discrete & Computational Geometry 7 Revista Matemática Iberoamericana 7 Journal of the Ramanujan Mathematical Society 7 Indagationes Mathematicae. New Series 7 Applicable Algebra in Engineering, Communication and Computing 7 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 7 Acta Mathematica Sinica. English Series 7 Journal of High Energy Physics 7 Integers 7 Cryptography and Communications 6 American Mathematical Monthly 6 Discrete Mathematics 6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 6 Canadian Mathematical Bulletin 6 Illinois Journal of Mathematics 6 Nagoya Mathematical Journal 6 Osaka Journal of Mathematics 6 Linear Algebra and its Applications 6 Expositiones Mathematicae 6 Selecta Mathematica. New Series 6 Discrete and Continuous Dynamical Systems 6 Documenta Mathematica 6 JP Journal of Algebra, Number Theory and Applications 5 Nuclear Physics. B 5 Journal of Geometry and Physics 5 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5 Applied Mathematics and Computation 5 Bulletin de la Société Mathématique de France 5 Czechoslovak Mathematical Journal 5 Journal of the London Mathematical Society. Second Series 5 Proceedings of the Edinburgh Mathematical Society. Series II 5 Results in Mathematics 5 Tokyo Journal of Mathematics 5 Journal of Mathematical Sciences (New York) 5 Journal of the Australian Mathematical Society 5 Journal of the Institute of Mathematics of Jussieu 5 Advances in Mathematics of Communications 5 Science China. Mathematics 5 Kyoto Journal of Mathematics ...and 204 more Serials
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### Cited in 56 Fields

 1,955 Number theory (11-XX) 1,199 Algebraic geometry (14-XX) 346 Dynamical systems and ergodic theory (37-XX) 278 Information and communication theory, circuits (94-XX) 87 Field theory and polynomials (12-XX) 75 Computer science (68-XX) 66 Quantum theory (81-XX) 64 Group theory and generalizations (20-XX) 55 Several complex variables and analytic spaces (32-XX) 50 Commutative algebra (13-XX) 38 Combinatorics (05-XX) 35 Special functions (33-XX) 33 Associative rings and algebras (16-XX) 32 Functions of a complex variable (30-XX) 28 Mathematical logic and foundations (03-XX) 24 Algebraic topology (55-XX) 18 $$K$$-theory (19-XX) 18 Convex and discrete geometry (52-XX) 17 Geometry (51-XX) 15 Numerical analysis (65-XX) 14 Topological groups, Lie groups (22-XX) 14 Difference and functional equations (39-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Functional analysis (46-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 Manifolds and cell complexes (57-XX) 11 Nonassociative rings and algebras (17-XX) 10 Probability theory and stochastic processes (60-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 History and biography (01-XX) 9 Ordinary differential equations (34-XX) 9 Differential geometry (53-XX) 6 General and overarching topics; collections (00-XX) 6 Relativity and gravitational theory (83-XX) 4 General algebraic systems (08-XX) 4 Category theory; homological algebra (18-XX) 4 Real functions (26-XX) 4 Operator theory (47-XX) 4 Mechanics of particles and systems (70-XX) 3 Measure and integration (28-XX) 3 Potential theory (31-XX) 2 Partial differential equations (35-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operations research, mathematical programming (90-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)

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