Edit Profile (opens in new tab) Silverman, Joseph Hillel Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0585.14026Silverman, Joseph H. 824 1986 The arithmetic of elliptic curves. 2nd ed. Zbl 1194.11005Silverman, Joseph H. 466 2009 Advanced topics in the arithmetic of elliptic curves. Zbl 0911.14015Silverman, Joseph H. 404 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 1159.11001Hardy, G. H.; Wright, E. M. 311 2008 Diophantine geometry. An introduction. Zbl 0948.11023Hindry, Marc; Silverman, Joseph H. 187 2000 The arithmetic of dynamical systems. Zbl 1130.37001Silverman, Joseph H. 182 2007 Handbook of finite fields. Zbl 1319.11001 150 2013 Rational points on elliptic curves. Zbl 0752.14034Silverman, Joseph H.; Tate, John 108 1992 NTRU: A ring-based public key cryptosystem. Zbl 1067.94538Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H. 97 1998 Canonical heights on varieties with morphisms. Zbl 0826.14015Call, Gregory S.; Silverman, Joseph H. 85 1993 Wieferich’s criterion and the abc-conjecture. Zbl 0654.10019Silverman, Joseph H. 61 1988 Heights and the specialization map for families of abelian varieties. Zbl 0505.14035Silverman, Joseph H. 59 1983 Rational periodic points of rational functions. Zbl 0819.11045Morton, Patrick; Silverman, Joseph H. 57 1994 The canonical height and integral points on elliptic curves. Zbl 0657.14018Hindry, M.; Silverman, J. H. 50 1988 The difference between the Weil height and the canonical height on elliptic curves. Zbl 0729.14026Silverman, Joseph H. 44 1990 Lower bounds for height functions. Zbl 0579.14035Silverman, Joseph H. 41 1984 The space of rational maps on \(\mathbf P^1\). Zbl 0966.14031Silverman, Joseph H. 40 1998 Periodic points, multiplicities, and dynamical units. Zbl 0813.11059Morton, Patrick; Silverman, Joseph H. 39 1995 Computig heights on elliptic curves. Zbl 0656.14016Silverman, Joseph H. 38 1988 Integer points, diophantine approximation, and iteration of rational maps. Zbl 0811.11052Silverman, Joseph H. 37 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 36 1986 Rational points on K3 surfaces: A new canonical height. Zbl 0754.14023Silverman, Joseph H. 31 1991 Lower bound for the canonical height on elliptic curves. Zbl 0475.14033Silverman, Joseph H. 30 1981 An introduction to mathematical cryptography. Zbl 1160.94001Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H. 29 2008 Bielliptic curves and symmetric products. Zbl 0727.11023Harris, Joe; Silverman, Joseph H. 27 1991 Primitive divisors in arithmetic dynamics. Zbl 1242.11012Ingram, Patrick; Silverman, Joseph H. 26 2009 Arithmetic distance functions and height functions in diophantine geometry. Zbl 0607.14013Silverman, Joseph H. 26 1987 The number of elliptic curves over \(\mathbb{Q}\) with conductor \(N\). Zbl 0868.11029Brumer, Armand; Silverman, Joseph H. 24 1996 Generalized greatest common divisors, divisibility sequences, and Vojta’s conjecture for blowups. Zbl 1197.11070Silverman, Joseph H. 22 2005 NTRUSign: Digital signatures using the NTRU lattice. Zbl 1039.94525Hoffstein, Jeffrey; Howgrave-Graham, Nick; Pipher, Jill; Silverman, Joseph H.; Whyte, William 21 2003 On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties. Zbl 1393.37115Kawaguchi, Shu; Silverman, Joseph H. 21 2016 Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\). Zbl 1009.11035Bremner, A.; Silverman, J. H.; Tzanakis, N. 20 2000 Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. Zbl 1372.37093Silverman, Joseph H. 20 2014 Divisibility of the specialization map for families of elliptic curves. Zbl 0613.14029Silverman, Joseph H. 18 1985 Moduli spaces and arithmetic dynamics. Zbl 1247.37004Silverman, Joseph H. 18 2012 An inequality relating the regulator and the discriminant of a number field. Zbl 0552.12003Silverman, Joseph H. 17 1984 The field of definition for dynamical systems on \(\mathbb{P}^ 1\). Zbl 0849.11090Silverman, Joseph H. 17 1995 Uniform bounds for the number of solutions to \(Y^ n=f(X)\). Zbl 0611.10009Evertse, J.-H.; Silverman, J. H. 16 1986 The S-unit equation over function fields. Zbl 0533.10013Silverman, Joseph H. 15 1984 Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties. Zbl 1391.37078Kawaguchi, Shu; Silverman, Joseph H. 15 2016 Rational points on elliptic curves. 2nd ed. Zbl 1346.11001Silverman, Joseph H.; Tate, John T. 14 2015 On the distribution of integer points on curves of genus zero. Zbl 0979.11037Silverman, J. H. 14 2000 The Markoff equation \(X^ 2+Y^ 2+Z^ 2=aXYZ\) over quadratic imaginary fields. Zbl 0702.11012Silverman, Joseph H. 13 1990 Examples of dynamical degree equals arithmetic degree. Zbl 1309.37084Kawaguchi, Shu; Silverman, Joseph H. 13 2014 Integer points and the rank of Thue elliptic curves. Zbl 0494.14008Silverman, Joseph H. 12 1982 Arithmetic and dynamical degrees on abelian varieties. Zbl 1416.11091Silverman, Joseph H. 12 2017 Variation of periods modulo \(p\) in arithmetic dynamics. Zbl 1153.11028Silverman, Joseph H. 12 2008 Geometric and arithmetic properties of the Hénon map. Zbl 0807.58021Silverman, Joseph H. 12 1994 A quantitative version of Siegel’s theorem: integral points on elliptic curves and Catalan curves. Zbl 0608.14021Silverman, Joseph H. 12 1987 Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Paperback ed. Zbl 1051.11500 12 2000 Integer points on curves of genus 1. Zbl 0487.10015Silverman, Joseph H. 12 1983 On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504Shparlinski, Igor E.; Silverman, Joseph H. 12 2001 Common divisors of elliptic divisibility sequences over function fields. Zbl 1128.11015Silverman, Joseph H. 11 2004 On the rank of an elliptic surface. Zbl 0905.14019Rosen, Michael; Silverman, Joseph H. 11 1998 Representations of integers by binary forms and the rank of the Mordell- Weil group. Zbl 0525.14012Silverman, J. H. 11 1983 Dynamics of projective morphisms having identical canonical heights. Zbl 1130.11035Kawaguchi, Shu; Silverman, Joseph H. 11 2007 Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092Ingram, Patrick; Silverman, Joseph H. 11 2012 Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture. Zbl 1297.37046Silverman, Joseph H. 11 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 0993.11028Hindry, Marc; Silverman, Joseph 10 1999 Choosing parameters for NTRUEncrypt. Zbl 1383.94022Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei 10 2017 An upper bound for the conductor of an abelian variety. Zbl 0816.14021Lockhart, Paul; Rosen, Michael; Silverman, Joseph H. 10 1993 Heights and elliptic curves. Zbl 0603.14020Silverman, Joseph H. 10 1986 The Xedni calculus and the elliptic curve discrete logarithm problem. Zbl 0948.11049Silverman, Joseph H. 10 2000 Exceptional units and numbers of small Mahler measure. Zbl 0851.11064Silverman, Joseph H. 10 1995 \(p\)-adic properties of division polynomials and elliptic divisibility sequences. Zbl 1066.11024Silverman, Joseph H. 10 2005 NSS: an NTRU lattice-based signature scheme. Zbl 0981.94039Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H. 10 2001 Nonarchimedean Green functions and dynamics on projective space. Zbl 1161.32009Kawaguchi, Shu; Silverman, Joseph H. 9 2009 A lower bound for the canonical height on abelian varieties over abelian extensions. Zbl 1060.11041Baker, Matthew H.; Silverman, Joseph H. 9 2004 Analysis of the Xedni calculus attack. Zbl 0948.11048Jacobson, Michael J.; Koblitz, Neal; Silverman, Joseph H.; Stein, Andreas; Teske, Edlyn 9 2000 On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024Rosen, Michael; Silverman, Joseph H. 9 2007 Current trends and open problems in arithmetic dynamics. Zbl 1468.37001Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J. 9 2019 The average rank of an algebraic family of elliptic curves. Zbl 0923.11087Silverman, Joseph H. 8 1998 A lower bound for the canonical height on elliptic curves over abelian extensions. Zbl 1053.11052Silverman, Joseph H. 8 2004 On Lehmer’s conjecture for elliptic curves. Zbl 0741.14013Hindry, Marc; Silverman, Joseph H. 8 1990 On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture. Zbl 1347.37153Silverman, Joseph H.; Viray, Bianca 8 2013 Variations on a theme of Romanoff. Zbl 0869.11004Murty, M. Ram; Rosen, Michael; Silverman, Joseph H. 8 1996 The impact of decryption failures on the security of NTRU encryption. Zbl 1122.94377Howgrave-Graham, Nick; Nguyen, Phong Q.; Pointcheval, David; Proos, John; Silverman, Joseph H.; Singer, Ari; Whyte, William 8 2003 Terms in elliptic divisibility sequences divisible by their indices. Zbl 1225.11079Silverman, Joseph H.; Stange, Katherine E. 7 2011 A local-global criterion for dynamics on \({\mathbb P}^1\). Zbl 1243.37066Silverman, Joseph H.; Voloch, José Felipe 7 2009 Computing rational points on rank 1 elliptic curves via \(L\)-series and canonical heights. Zbl 1042.11036Silverman, Joseph H. 7 1999 Dimension reduction methods for convolution modular lattices. Zbl 1006.11033May, Alexander; Silverman, Joseph H. 7 2001 Amicable pairs and aliquot cycles for elliptic curves. Zbl 1269.11056Silverman, Joseph H.; Stange, Katherine E. 7 2011 The rank of elliptic surfaces in unramified abelian towers. Zbl 1105.11016Silverman, Joseph H. 7 2004 Rational points on certain families of curves of genus at least 2. Zbl 0642.14006Silverman, Joseph H. 7 1987 Small Salem numbers, exceptional units, and Lehmer’s conjecture. Zbl 0883.11045Silverman, Joseph H. 7 1996 Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Zbl 0878.11004 7 1997 Computing canonical heights with little (or no) factorization. Zbl 0898.11021Silverman, Joseph H. 7 1997 Common divisors of \(a^n-1\) and \(b^n-1\) over function fields. Zbl 1120.11045Silverman, Joseph H. 7 2004 Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. Zbl 1079.94553Howgrave-Graham, Nick; Silverman, Joseph H.; Whyte, William 7 2005 The Neron fiber of Abelian varieties with potential good reduction. Zbl 0497.14016Silverman, Joseph H. 6 1983 Taxicabs and sums of two cubes. Zbl 0796.11022Silverman, Joseph H. 6 1993 The sign of an elliptic divisibility sequence. Zbl 1148.11013Silverman, Joseph H.; Stephens, Nelson 6 2006 \(S\)-integer points on elliptic curves. Zbl 0824.11038Gross, Robert; Silverman, Joseph 6 1995 Elliptic curve discrete logarithms and the index calculus. Zbl 0944.11043Silverman, Joseph H.; Suzuki, Joe 5 1998 The Catalan equation over function fields. Zbl 0493.10020Silverman, Joseph H. 5 1982 Hecke points on modular curves. Zbl 0744.14014Silverman, Joseph H. 5 1990 Height estimates for equidimensional dominant rational maps. Zbl 1311.11057Silverman, Joseph H. 5 2011 Some arithmetic properties of Weierstrass points: Hyperelliptic curves. Zbl 0758.14023Silverman, Joseph H. 5 1990 A bound for the Mordell-Weil rank of an elliptic surface after a cyclic base extension. Zbl 0951.14023Silverman, Joseph H. 5 2000 Random small Hamming weight products with applications to cryptography. Zbl 1028.94023Hoffstein, Jeffrey; Silverman, Joseph H. 5 2003 Moduli spaces for dynamical systems with portraits. Zbl 1448.37132Doyle, John R.; Silverman, Joseph H. 4 2020 Erratum to “On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties”. Zbl 1439.37090Kawaguchi, Shu; Silverman, Joseph H. 1 2020 GIT stability of Hénon maps. Zbl 1448.37133Lee, Chong Gyu; Silverman, Joseph H. 1 2020 Current trends and open problems in arithmetic dynamics. Zbl 1468.37001Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J. 9 2019 A uniform field-of-definition/field-of-moduli bound for dynamical systems on \(\mathbb{P}^N\). Zbl 1432.37124Doyle, John R.; Silverman, Joseph H. 2 2019 A classification of degree \(2\) semi-stable rational maps \(\mathbb{P}^2\rightarrow\mathbb{P}^2\) with large finite dynamical automorphism group. Zbl 1432.37123Manes, Michelle; Silverman, Joseph H. 1 2019 Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures. Zbl 1396.37097Silverman, Joseph H. 3 2018 Degeneration of dynamical degrees in families of maps. Zbl 1404.37123Silverman, Joseph H.; Call, Gregory S. 1 2018 Fully homomorphic encryption from the finite field isomorphism problem. Zbl 1385.94032Doröz, Yarkın; Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.; Sunar, Berk; Whyte, William; Zhang, Zhenfei 1 2018 Arithmetic and dynamical degrees on abelian varieties. Zbl 1416.11091Silverman, Joseph H. 12 2017 Choosing parameters for NTRUEncrypt. Zbl 1383.94022Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei 10 2017 Finite ramification for preimage fields of post-critically finite morphisms. Zbl 1391.14004Bridy, Andrew; Ingram, Patrick; Jones, Rafe; Juul, Jamie; Levy, Alon; Manes, Michelle; Rubinstein-Salzedo, Simon; Silverman, Joseph H. 4 2017 Rational points on, and the arithmetic of, elliptic curves: a tale of two books (and an article). Zbl 1436.11005Silverman, Joseph H. 1 2017 On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties. Zbl 1393.37115Kawaguchi, Shu; Silverman, Joseph H. 21 2016 Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties. Zbl 1391.37078Kawaguchi, Shu; Silverman, Joseph H. 15 2016 Rational points on elliptic curves. 2nd ed. Zbl 1346.11001Silverman, Joseph H.; Tate, John T. 14 2015 Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. Zbl 1372.37093Silverman, Joseph H. 20 2014 Examples of dynamical degree equals arithmetic degree. Zbl 1309.37084Kawaguchi, Shu; Silverman, Joseph H. 13 2014 Transcript secure signatures based on modular lattices. Zbl 1380.94099Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William 5 2014 An introduction to mathematical cryptography. 2nd ed. Zbl 1297.94001Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H. 2 2014 Practical signatures from the partial Fourier recovery problem. Zbl 1356.94060Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William 1 2014 Handbook of finite fields. Zbl 1319.11001 150 2013 Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture. Zbl 1297.37046Silverman, Joseph H. 11 2013 On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture. Zbl 1347.37153Silverman, Joseph H.; Viray, Bianca 8 2013 What is …the \(p\)-adic Mandelbrot set? Zbl 1322.28001Silverman, Joseph H. 1 2013 Moduli spaces and arithmetic dynamics. Zbl 1247.37004Silverman, Joseph H. 18 2012 Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092Ingram, Patrick; Silverman, Joseph H. 11 2012 Algebraic divisibility sequences over function fields. Zbl 1251.11008Ingram, Patrick; Mahé, Valéry; Silverman, Joseph H.; Stange, Katherine E.; Streng, Marco 5 2012 Elliptic Carmichael numbers and elliptic Korselt criteria. Zbl 1304.11047Silverman, Joseph H. 5 2012 An algebraic approach to certain cases of Thurston rigidity. Zbl 1291.37072Silverman, Joseph H. 2 2012 Terms in elliptic divisibility sequences divisible by their indices. Zbl 1225.11079Silverman, Joseph H.; Stange, Katherine E. 7 2011 Amicable pairs and aliquot cycles for elliptic curves. Zbl 1269.11056Silverman, Joseph H.; Stange, Katherine E. 7 2011 Height estimates for equidimensional dominant rational maps. Zbl 1311.11057Silverman, Joseph H. 5 2011 A quantitative estimate for quasiintegral points in orbits. Zbl 1272.37039Hsia, Liang-Chung; Silverman, Joseph H. 4 2011 Lang’s height conjecture and Szpiro’s conjecture. Zbl 1304.11046Silverman, Joseph H. 1 2010 The arithmetic of elliptic curves. 2nd ed. Zbl 1194.11005Silverman, Joseph H. 466 2009 Primitive divisors in arithmetic dynamics. Zbl 1242.11012Ingram, Patrick; Silverman, Joseph H. 26 2009 Nonarchimedean Green functions and dynamics on projective space. Zbl 1161.32009Kawaguchi, Shu; Silverman, Joseph H. 9 2009 A local-global criterion for dynamics on \({\mathbb P}^1\). Zbl 1243.37066Silverman, Joseph H.; Voloch, José Felipe 7 2009 On a dynamical Brauer-Manin obstruction. Zbl 1196.37131Hsia, Liang-Chung; Silverman, Joseph 4 2009 Canonical heights and the arithmetic complexity of morphisms on projective space. Zbl 1221.11152Kawaguchi, Shu; Silverman, Joseph H. 2 2009 Lifting and elliptic curve discrete logarithms. Zbl 1256.94065Silverman, Joseph H. 1 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 1159.11001Hardy, G. H.; Wright, E. M. 311 2008 An introduction to mathematical cryptography. Zbl 1160.94001Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H. 29 2008 Variation of periods modulo \(p\) in arithmetic dynamics. Zbl 1153.11028Silverman, Joseph H. 12 2008 The arithmetic of dynamical systems. Zbl 1130.37001Silverman, Joseph H. 182 2007 Dynamics of projective morphisms having identical canonical heights. Zbl 1130.11035Kawaguchi, Shu; Silverman, Joseph H. 11 2007 On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024Rosen, Michael; Silverman, Joseph H. 9 2007 The sign of an elliptic divisibility sequence. Zbl 1148.11013Silverman, Joseph H.; Stephens, Nelson 6 2006 Height bounds and preperiodic points for families of jointly regular affine maps. Zbl 1154.11328Silverman, Joseph H. 2 2006 Timing attacks on NTRUEncrypt via variation in the number of hash calls. Zbl 1177.94174Silverman, Joseph H.; Whyte, William 2 2006 Generalized greatest common divisors, divisibility sequences, and Vojta’s conjecture for blowups. Zbl 1197.11070Silverman, Joseph H. 22 2005 \(p\)-adic properties of division polynomials and elliptic divisibility sequences. Zbl 1066.11024Silverman, Joseph H. 10 2005 Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. Zbl 1079.94553Howgrave-Graham, Nick; Silverman, Joseph H.; Whyte, William 7 2005 An algebraic approach to NTRU (\(q = 2^{n}\)) via Witt vectors and overdetermined systems of nonlinear equations. Zbl 1116.94333Silverman, J. H.; Smart, N. P.; Vercauteren, F. 1 2005 Common divisors of elliptic divisibility sequences over function fields. Zbl 1128.11015Silverman, Joseph H. 11 2004 A lower bound for the canonical height on abelian varieties over abelian extensions. Zbl 1060.11041Baker, Matthew H.; Silverman, Joseph H. 9 2004 A lower bound for the canonical height on elliptic curves over abelian extensions. Zbl 1053.11052Silverman, Joseph H. 8 2004 The rank of elliptic surfaces in unramified abelian towers. Zbl 1105.11016Silverman, Joseph H. 7 2004 Common divisors of \(a^n-1\) and \(b^n-1\) over function fields. Zbl 1120.11045Silverman, Joseph H. 7 2004 NTRUSign: Digital signatures using the NTRU lattice. Zbl 1039.94525Hoffstein, Jeffrey; Howgrave-Graham, Nick; Pipher, Jill; Silverman, Joseph H.; Whyte, William 21 2003 The impact of decryption failures on the security of NTRU encryption. Zbl 1122.94377Howgrave-Graham, Nick; Nguyen, Phong Q.; Pointcheval, David; Proos, John; Silverman, Joseph H.; Singer, Ari; Whyte, William 8 2003 Random small Hamming weight products with applications to cryptography. Zbl 1028.94023Hoffstein, Jeffrey; Silverman, Joseph H. 5 2003 On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504Shparlinski, Igor E.; Silverman, Joseph H. 12 2001 NSS: an NTRU lattice-based signature scheme. Zbl 0981.94039Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H. 10 2001 Dimension reduction methods for convolution modular lattices. Zbl 1006.11033May, Alexander; Silverman, Joseph H. 7 2001 Optimizations for NTRU. Zbl 0987.94027Hoffstein, Jeffrey; Silverman, Joseph 3 2001 Polynomial rings and efficient public key authentication. II. Zbl 1002.94535Hoffstein, Jeffrey; Silverman, Joseph H. 1 2001 NTRU in constrained devices. Zbl 1012.94548Bailey, Daniel V.; Coffin, Daniel; Elbirt, Adam; Silverman, Joseph H.; Woodbury, Adam D. 1 2001 Cryptography and lattices. 1st international conference, CaLC 2001, Providence, RI, USA, March 29–30, 2001. Revised papers. Zbl 0971.00060 1 2001 Diophantine geometry. An introduction. Zbl 0948.11023Hindry, Marc; Silverman, Joseph H. 187 2000 Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\). Zbl 1009.11035Bremner, A.; Silverman, J. H.; Tzanakis, N. 20 2000 On the distribution of integer points on curves of genus zero. Zbl 0979.11037Silverman, J. H. 14 2000 Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Paperback ed. Zbl 1051.11500 12 2000 The Xedni calculus and the elliptic curve discrete logarithm problem. Zbl 0948.11049Silverman, Joseph H. 10 2000 Analysis of the Xedni calculus attack. Zbl 0948.11048Jacobson, Michael J.; Koblitz, Neal; Silverman, Joseph H.; Stein, Andreas; Teske, Edlyn 9 2000 A bound for the Mordell-Weil rank of an elliptic surface after a cyclic base extension. Zbl 0951.14023Silverman, Joseph H. 5 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 0993.11028Hindry, Marc; Silverman, Joseph 10 1999 Computing rational points on rank 1 elliptic curves via \(L\)-series and canonical heights. Zbl 1042.11036Silverman, Joseph H. 7 1999 Fast multiplication in finite fields GF\((2^N)\). Zbl 0993.11065Silverman, Joseph H. 3 1999 Divisibility of the specialization map for twists of abelian varieties. Zbl 0938.11030Silverman, Joseph H. 1 1999 NTRU: A ring-based public key cryptosystem. Zbl 1067.94538Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H. 97 1998 The space of rational maps on \(\mathbf P^1\). Zbl 0966.14031Silverman, Joseph H. 40 1998 On the rank of an elliptic surface. Zbl 0905.14019Rosen, Michael; Silverman, Joseph H. 11 1998 The average rank of an algebraic family of elliptic curves. Zbl 0923.11087Silverman, Joseph H. 8 1998 Elliptic curve discrete logarithms and the index calculus. Zbl 0944.11043Silverman, Joseph H.; Suzuki, Joe 5 1998 Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Zbl 0878.11004 7 1997 Computing canonical heights with little (or no) factorization. Zbl 0898.11021Silverman, Joseph H. 7 1997 A friendly introduction to number theory. Zbl 0973.11003Silverman, Joseph H. 1 1997 The number of elliptic curves over \(\mathbb{Q}\) with conductor \(N\). Zbl 0868.11029Brumer, Armand; Silverman, Joseph H. 24 1996 Variations on a theme of Romanoff. Zbl 0869.11004Murty, M. Ram; Rosen, Michael; Silverman, Joseph H. 8 1996 Small Salem numbers, exceptional units, and Lehmer’s conjecture. Zbl 0883.11045Silverman, Joseph H. 7 1996 Rational functions with a polynomial iterate. Zbl 0848.11049Silverman, Joseph H. 4 1996 Computing the canonical height on K3 surfaces. Zbl 0865.14020Call, Gregory S.; Silverman, Joseph H. 3 1996 Periodic points, multiplicities, and dynamical units. Zbl 0813.11059Morton, Patrick; Silverman, Joseph H. 39 1995 The field of definition for dynamical systems on \(\mathbb{P}^ 1\). Zbl 0849.11090Silverman, Joseph H. 17 1995 Exceptional units and numbers of small Mahler measure. Zbl 0851.11064Silverman, Joseph H. 10 1995 \(S\)-integer points on elliptic curves. Zbl 0824.11038Gross, Robert; Silverman, Joseph 6 1995 Counting integer and rational points on varieties. Zbl 0834.11029Silverman, Joseph H. 1 1995 Advanced topics in the arithmetic of elliptic curves. Zbl 0911.14015Silverman, Joseph H. 404 1994 ...and 47 more Documents all cited Publications top 5 cited Publications 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 all top 5 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. 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Mathematics 5 Kyoto Journal of Mathematics ...and 204 more Serials all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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