Edit Profile (opens in new tab) Stein, William A. Co-Author Distance Author ID: stein.william-a Published as: Stein, William A.; Stein, William External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 46 Publications since 2000, including 3 Books 2 Further Contributions Software Indexed: 2 Packages Biographic References: 1 Publication Co-Authors: 34 Co-Authors with 28 Joint Publications 793 Co-Co-Authors all top 5 Co-Authors 9 single-authored 5 Agashe, Amod 4 Mazur, Barry 4 Watkins, Mark James 3 Balakrishnan, Jennifer S. 3 Ribet, Kenneth Alan 2 Conrad, Brian 2 Cremona, John E. 2 Jetchev, Dimitar P. 2 Stoll, Michael 1 Bektemirov, Baur 1 Bober, Jonathan W. 1 Bradshaw, Robert W. 1 Buzzard, Kevin 1 Calegari, Frank 1 Çiperiani, Mirela 1 Coates, John Henry 1 Coleman, Robert Frederick 1 Deines-Schartz, Alyson 1 Demeyer, Jeroen 1 Derickx, Maarten 1 Diaz-Lopez, Alexander 1 Dokchitser, Tim 1 Dummigan, Neil 1 Edixhoven, Sebastiaan Johan 1 Eröcal, Burçin 1 Flynn, Eugene Victor 1 Grigorov, Grigor 1 Gunnells, Paul E. 1 Ho, Wei 1 Jorza, Andrei 1 Joyner, David 1 Kamienny, Sheldon 1 Kaplan, Nathan 1 Klages-Mundt, Ariah 1 Kohel, David R. 1 Koo, Koopa Tak-Lun 1 Lario, Joan-Carles 1 Lauter, Kristin Estella 1 Leprévost, Franck 1 Lévêque, Benjamin 1 Liang, Zhibin 1 Merel, Loïc 1 Müller, Jan Steffen 1 Ohana, R. Andrew 1 Patrikis, Stefan T. 1 Pernet, Clément 1 Rabindranath, Ashwath 1 Schaefer, Edward F. 1 Schoof, René 1 Sharaba, Paul 1 Spicer, Simon 1 Sujatha, Ramdorai 1 Tarniţǎ, Corina E. 1 Tate, John Torrence jun. 1 Verrill, Helena A. 1 Weigandt, James E. 1 Whitcher, Ursula A. 1 Wiese, Gabor 1 Wuthrich, Christian all top 5 Serials 6 Mathematics of Computation 4 Journal of Number Theory 4 Documenta Mathematica 3 IMRN. International Mathematics Research Notices 2 Notices of the American Mathematical Society 2 LMS Journal of Computation and Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 SIGSAM Bulletin 1 Bulletin of the American Mathematical Society. New Series 1 Experimental Mathematics 1 Journal de Théorie des Nombres de Bordeaux 1 Mathematical Research Letters 1 Pure and Applied Mathematics Quarterly 1 Graduate Studies in Mathematics 1 Algebra & Number Theory 1 Undergraduate Texts in Mathematics all top 5 Fields 42 Number theory (11-XX) 8 Algebraic geometry (14-XX) 5 Computer science (68-XX) 2 Numerical analysis (65-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 42 Publications have been cited 326 times in 258 Documents Cited by ▼ Year ▼ Modular forms, a computational approach. With an appendix by Paul E. Gunnells. Zbl 1110.11015 Stein, William 188 2007 SAGE: system for algebra and geometry experimentation. Zbl 1341.68315 Stein, William; Joyner, David 29 2005 \(J_1(p)\) has connected fibers. Zbl 1101.14311 Conrad, Brian; Edixhoven, Bas; Stein, William 25 2003 Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. Zbl 1020.11043 Flynn, E. Victor; Leprévost, Franck; Schaefer, Edward F.; Stein, William A.; Stoll, Michael 24 2001 The Manin constant. (With an appendix by J. Cremona). Zbl 1109.11032 Agashe, Amod; Ribet, Kenneth; Stein, William A. 24 2006 Computation of \(p\)-adic heights and log convergence. Zbl 1135.11034 Mazur, Barry; Stein, William; Tate, John 22 2007 Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032 Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark 22 2007 Torsion points on elliptic curves over number fields of small degree. Zbl 1536.11084 Derickx, Maarten; Kamienny, Sheldon; Stein, William; Stoll, Michael 22 2023 Lectures on Serre’s conjectures. Zbl 1160.11327 Ribet, Kenneth A.; Stein, William A. 18 2001 Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero. With an Appendix by J. Cremona and B. Mazur. Zbl 1084.11033 Agashe, Amod; Stein, William 18 2005 Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves. Zbl 1209.11059 Grigorov, Grigor; Jorza, Andrei; Patrikis, Stefan; Stein, William A.; Tarnita, Corina 16 2009 A database of elliptic curves – first report. Zbl 1058.11036 Stein, William A.; Watkins, Mark 16 2002 The modular degree, congruence primes, and multiplicity one. Zbl 1276.11087 Agashe, Amod; Ribet, Kenneth A.; Stein, William A. 16 2012 Component groups of purely toric quotients. Zbl 1081.11040 Conrad, Brian; Stein, William A. 12 2001 Algorithms for the arithmetic of elliptic curves using Iwasawa theory. Zbl 1336.11047 Stein, William; Wuthrich, Christian 12 2013 Visibility of Shafarevich-Tate groups of abelian varieties. Zbl 1101.14055 Agashe, Amod; Stein, William 12 2002 Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks. Zbl 1391.11077 Balakrishnan, Jennifer S.; Ho, Wei; Kaplan, Nathan; Spicer, Simon; Stein, William; Weigandt, James 10 2016 Fast computation of Hermite normal forms of random integer matrices. Zbl 1206.15027 Pernet, Clément; Stein, William 9 2010 Modular parametrizations of Neumann-Setzer elliptic curves. Zbl 1088.11043 Stein, William; Watkins, Mark 8 2004 The field generated by the points of small prime order on an elliptic curve. Zbl 1027.11041 Merel, Loïc; Stein, William A. 8 2001 Elementary number theory. Primes, congruences, and secrets. A computational approach. Zbl 1155.11002 Stein, William 8 2009 A \(p\)-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties. Zbl 1402.11099 Balakrishnan, Jennifer S.; Müller, J. Steffen; Stein, William A. 8 2016 Shafarevich-Tate groups of nonsquare order. Zbl 1080.11047 Stein, William A. 7 2004 On the generation of the coefficient field of a newform by a single Hecke eigenvalue. Zbl 1171.11027 Koo, Koopa Tak-Lun; Stein, William; Wiese, Gabor 6 2008 The Sage project: unifying free mathematical software to create a viable alternative to Magma, Maple, Mathematica and Matlab. Zbl 1295.68225 Eröcal, Burçin; Stein, William 5 2010 Conjectures about discriminants of Hecke algebras of prime level. Zbl 1125.11320 Calegari, Frank; Stein, William A. 5 2004 Prime numbers and the Riemann hypothesis. Zbl 1356.11001 Mazur, Barry; Stein, William 5 2016 Sage: creating a viable free open source alternative to Magma, Maple, Mathematica, and MATLAB. Zbl 1316.65123 Stein, William 4 2013 There are genus one curves over \({\mathbb Q}\) of every odd index. Zbl 1002.11050 Stein, William A. 4 2002 Explicit Heegner points: Kolyvagin’s conjecture and non-trivial elements in the Shafarevich-Tate group. Zbl 1228.11082 Jetchev, Dimitar; Lauter, Kristin; Stein, William 4 2009 Constructing elements in Shafarevich-Tate groups of modular motives. Zbl 1161.11354 Dummigan, Neil; Stein, William; Watkins, Mark 4 2003 A database of elliptic curves over \(\mathbb Q(\sqrt{5})\): a first report. Zbl 1344.11045 Bober, Jonathan; Deines, Alyson; Klages-Mundt, Ariah; LeVeque, Benjamin; Ohana, R. Andrew; Rabindranath, Ashwath; Sharaba, Paul; Stein, William 3 2013 Approximation of eigenforms of infinite slope by eigenforms of finite slope. Zbl 1101.11015 Coleman, Robert F.; Stein, William A. 3 2004 Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein. Zbl 1116.11310 Lario, Joan-C.; Schoof, René 3 2002 A mod five approach to modularity of icosahedral Galois representations. Zbl 1054.11028 Buzzard, Kevin; Stein, William A. 3 2002 Non-commutative Iwasawa theory for modular forms. Zbl 1291.11089 Coates, John H.; Dokchitser, Tim; Liang, Zhibin; Stein, William; Sujatha, R. 2 2013 Component groups of quotients of \(J_0(N)\). Zbl 0984.11022 Kohel, David R.; Stein, William A. 2 2000 Cuspidal modular symbols are transportable. Zbl 1049.11054 Stein, William A.; Verrill, Helena A. 2 2001 An introduction to computing modular forms using modular symbols. Zbl 1188.11074 Stein, William A. 2 2008 Heegner points and the arithmetic of elliptic curves over ring class extensions. Zbl 1276.11088 Bradshaw, Robert; Stein, William 2 2012 \(p\)-adic heights of Heegner points and \(\Lambda\)-adic regulators. Zbl 1316.11116 Balakrishnan, Jennifer S.; Çiperiani, Mirela; Stein, William 1 2015 Toward a generalization of the Gross-Zagier conjecture. Zbl 1278.11070 Stein, William A. 1 2011 Torsion points on elliptic curves over number fields of small degree. Zbl 1536.11084 Derickx, Maarten; Kamienny, Sheldon; Stein, William; Stoll, Michael 22 2023 Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks. Zbl 1391.11077 Balakrishnan, Jennifer S.; Ho, Wei; Kaplan, Nathan; Spicer, Simon; Stein, William; Weigandt, James 10 2016 A \(p\)-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties. Zbl 1402.11099 Balakrishnan, Jennifer S.; Müller, J. Steffen; Stein, William A. 8 2016 Prime numbers and the Riemann hypothesis. Zbl 1356.11001 Mazur, Barry; Stein, William 5 2016 \(p\)-adic heights of Heegner points and \(\Lambda\)-adic regulators. Zbl 1316.11116 Balakrishnan, Jennifer S.; Çiperiani, Mirela; Stein, William 1 2015 Algorithms for the arithmetic of elliptic curves using Iwasawa theory. Zbl 1336.11047 Stein, William; Wuthrich, Christian 12 2013 Sage: creating a viable free open source alternative to Magma, Maple, Mathematica, and MATLAB. Zbl 1316.65123 Stein, William 4 2013 A database of elliptic curves over \(\mathbb Q(\sqrt{5})\): a first report. Zbl 1344.11045 Bober, Jonathan; Deines, Alyson; Klages-Mundt, Ariah; LeVeque, Benjamin; Ohana, R. Andrew; Rabindranath, Ashwath; Sharaba, Paul; Stein, William 3 2013 Non-commutative Iwasawa theory for modular forms. Zbl 1291.11089 Coates, John H.; Dokchitser, Tim; Liang, Zhibin; Stein, William; Sujatha, R. 2 2013 The modular degree, congruence primes, and multiplicity one. Zbl 1276.11087 Agashe, Amod; Ribet, Kenneth A.; Stein, William A. 16 2012 Heegner points and the arithmetic of elliptic curves over ring class extensions. Zbl 1276.11088 Bradshaw, Robert; Stein, William 2 2012 Toward a generalization of the Gross-Zagier conjecture. Zbl 1278.11070 Stein, William A. 1 2011 Fast computation of Hermite normal forms of random integer matrices. Zbl 1206.15027 Pernet, Clément; Stein, William 9 2010 The Sage project: unifying free mathematical software to create a viable alternative to Magma, Maple, Mathematica and Matlab. Zbl 1295.68225 Eröcal, Burçin; Stein, William 5 2010 Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves. Zbl 1209.11059 Grigorov, Grigor; Jorza, Andrei; Patrikis, Stefan; Stein, William A.; Tarnita, Corina 16 2009 Elementary number theory. Primes, congruences, and secrets. A computational approach. Zbl 1155.11002 Stein, William 8 2009 Explicit Heegner points: Kolyvagin’s conjecture and non-trivial elements in the Shafarevich-Tate group. Zbl 1228.11082 Jetchev, Dimitar; Lauter, Kristin; Stein, William 4 2009 On the generation of the coefficient field of a newform by a single Hecke eigenvalue. Zbl 1171.11027 Koo, Koopa Tak-Lun; Stein, William; Wiese, Gabor 6 2008 An introduction to computing modular forms using modular symbols. Zbl 1188.11074 Stein, William A. 2 2008 Modular forms, a computational approach. With an appendix by Paul E. Gunnells. Zbl 1110.11015 Stein, William 188 2007 Computation of \(p\)-adic heights and log convergence. Zbl 1135.11034 Mazur, Barry; Stein, William; Tate, John 22 2007 Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032 Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark 22 2007 The Manin constant. (With an appendix by J. Cremona). Zbl 1109.11032 Agashe, Amod; Ribet, Kenneth; Stein, William A. 24 2006 SAGE: system for algebra and geometry experimentation. Zbl 1341.68315 Stein, William; Joyner, David 29 2005 Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero. With an Appendix by J. Cremona and B. Mazur. Zbl 1084.11033 Agashe, Amod; Stein, William 18 2005 Modular parametrizations of Neumann-Setzer elliptic curves. Zbl 1088.11043 Stein, William; Watkins, Mark 8 2004 Shafarevich-Tate groups of nonsquare order. Zbl 1080.11047 Stein, William A. 7 2004 Conjectures about discriminants of Hecke algebras of prime level. Zbl 1125.11320 Calegari, Frank; Stein, William A. 5 2004 Approximation of eigenforms of infinite slope by eigenforms of finite slope. Zbl 1101.11015 Coleman, Robert F.; Stein, William A. 3 2004 \(J_1(p)\) has connected fibers. Zbl 1101.14311 Conrad, Brian; Edixhoven, Bas; Stein, William 25 2003 Constructing elements in Shafarevich-Tate groups of modular motives. Zbl 1161.11354 Dummigan, Neil; Stein, William; Watkins, Mark 4 2003 A database of elliptic curves – first report. Zbl 1058.11036 Stein, William A.; Watkins, Mark 16 2002 Visibility of Shafarevich-Tate groups of abelian varieties. Zbl 1101.14055 Agashe, Amod; Stein, William 12 2002 There are genus one curves over \({\mathbb Q}\) of every odd index. Zbl 1002.11050 Stein, William A. 4 2002 Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein. Zbl 1116.11310 Lario, Joan-C.; Schoof, René 3 2002 A mod five approach to modularity of icosahedral Galois representations. Zbl 1054.11028 Buzzard, Kevin; Stein, William A. 3 2002 Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. Zbl 1020.11043 Flynn, E. Victor; Leprévost, Franck; Schaefer, Edward F.; Stein, William A.; Stoll, Michael 24 2001 Lectures on Serre’s conjectures. Zbl 1160.11327 Ribet, Kenneth A.; Stein, William A. 18 2001 Component groups of purely toric quotients. Zbl 1081.11040 Conrad, Brian; Stein, William A. 12 2001 The field generated by the points of small prime order on an elliptic curve. Zbl 1027.11041 Merel, Loïc; Stein, William A. 8 2001 Cuspidal modular symbols are transportable. Zbl 1049.11054 Stein, William A.; Verrill, Helena A. 2 2001 Component groups of quotients of \(J_0(N)\). Zbl 0984.11022 Kohel, David R.; Stein, William A. 2 2000 all cited Publications top 5 cited Publications all top 5 Cited by 297 Authors 12 Balakrishnan, Jennifer S. 9 Stein, William A. 8 Agashe, Amod 8 Mazur, Barry 8 Müller, Jan Steffen 7 Lozano-Robledo, Álvaro 7 Stoll, Michael 6 Najman, Filip 6 Wuthrich, Christian 5 Derickx, Maarten 5 Papikian, Mihran 5 Pasten, Hector V. 4 Fisher, Tom A. 4 Keller, Timo 4 Lorenzini, Dino J. 4 Ray, Anwesh 4 van Bommel, Raymond 4 Voight, John Michael 4 Vonk, Jan B. 3 Besser, Amnon 3 Calegari, Frank 3 Česnavičius, Kęstutis 3 Dieulefait, Luis Victor 3 Dogra, Netan 3 González-Jiménez, Enrique 3 Khawaja, Maleeha 3 Morrow, Jackson Salvatore 3 Ozman, Ekin 3 Paladino, Laura 3 Rouse, Jeremy A. 3 Rubin, Karl Cooper 3 Shankar, Arul 3 Siksek, Samir 3 Sutherland, Andrew V. 3 Tian, Peng 2 Ahlgren, Scott D. 2 Bennett, Michael A. 2 Best, Alex J. 2 Bhargava, Manjul 2 Bianchi, Francesca 2 Bourdon, Abbey 2 Bradshaw, Robert W. 2 Bruin, Nils 2 Bruin, Peter 2 Burns, David John 2 Byeon, Dongho 2 Caro, Jerson 2 Cremona, John E. 2 Dąbrowski, Andrzej Bogdan 2 Dalal, Tarun 2 Darmon, Henri René 2 Dokchitser, Tim 2 Dvornicich, Roberto 2 Flynn, Eugene Victor 2 Halle, Lars Halvard 2 Hashimoto, Sachi 2 Ho, Wei 2 Howe, Everett W. 2 Jorza, Andrei 2 Kamienny, Sheldon 2 Kazalicki, Matija 2 Kedlaya, Kiran Sridhara 2 Kim, Taekyung 2 Kirst, Peter 2 Kohen, Daniel 2 Kumar, Narasimha 2 Li, Wanlin 2 Lowry-Duda, David 2 Macias Castillo, Daniel 2 Martin, Kimball 2 Mascot, Nicolas 2 Matschke, Benjamin 2 Melistas, Mentzelos 2 Michaud-Jacobs, Philippe 2 Miller, Robert L. 2 Obus, Andrew 2 Pacetti, Ariel Martín 2 Padurariu, Oana 2 Parent, Pierre 2 Poonen, Bjorn 2 Rechnitzer, Andrew Daniel 2 Rotger, Victor 2 Schaefer, Edward F. 2 Shekhar, Sudhanshu 2 Silverberg, Alice 2 Stein, Oliver 2 Sun, Hae-Sang 2 Szymaszkiewicz, Lucjan 2 Tuitman, Jan 2 Vigni, Stefano 2 Von Känel, Rafael 2 Vukorepa, Borna 2 Weston, Tom 2 Wewers, Stefan 2 Yhee, Donggeon 2 Zureick-Brown, David 1 Adžaga, Nikola 1 Agarwal, Mahesh 1 Angelantonj, Carlo 1 Baig, Salman ...and 197 more Authors all top 5 Cited in 75 Serials 34 Journal of Number Theory 27 Mathematics of Computation 16 Research in Number Theory 10 Proceedings of the American Mathematical Society 7 Annales de l’Institut Fourier 6 Mathematische Annalen 6 Experimental Mathematics 6 Journal de Théorie des Nombres de Bordeaux 6 LMS Journal of Computation and Mathematics 6 International Journal of Number Theory 5 Journal of Algebra 5 Mathematische Zeitschrift 5 Transactions of the American Mathematical Society 5 Bulletin of the American Mathematical Society. New Series 5 Annals of Mathematics. Second Series 5 Forum of Mathematics, Sigma 4 Compositio Mathematica 4 Journal für die Reine und Angewandte Mathematik 4 Algebra & Number Theory 3 Israel Journal of Mathematics 3 Advances in Mathematics 3 Duke Mathematical Journal 3 The Ramanujan Journal 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Bulletin of the London Mathematical Society 2 Canadian Journal of Mathematics 2 Inventiones Mathematicae 2 Journal of the Mathematical Society of Japan 2 Manuscripta Mathematica 2 Memoirs of the American Mathematical Society 2 Journal of the Ramanujan Mathematical Society 2 Documenta Mathematica 2 Journal of the European Mathematical Society (JEMS) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 European Journal of Mathematics 1 Bulletin of the Australian Mathematical Society 1 Discrete Applied Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 The Mathematical Intelligencer 1 Acta Arithmetica 1 The Annals of Statistics 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Glasgow Mathematical Journal 1 Indiana University Mathematics Journal 1 Publications Mathématiques 1 Journal of the Korean Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Journal of Optimization Theory and Applications 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Tokyo Journal of Mathematics 1 Journal of Symbolic Computation 1 Revista Matemática Iberoamericana 1 Publicacions Matemàtiques 1 Journal of Global Optimization 1 Journal of Algebraic Geometry 1 The New York Journal of Mathematics 1 Selecta Mathematica. New Series 1 Journal of High Energy Physics 1 Central European Journal of Mathematics 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Statistical Mechanics: Theory and Experiment 1 Oberwolfach Reports 1 Involve 1 Annales Mathématiques du Québec 1 Transactions of the London Mathematical Society 1 Journal of Applied Mathematics, Statistics and Informatics 1 Research in the Mathematical Sciences 1 Journal de l’École Polytechnique – Mathématiques 1 Transactions of the American Mathematical Society. Series B 1 SIAM Journal on Applied Algebra and Geometry 1 Graduate Journal of Mathematics all top 5 Cited in 23 Fields 243 Number theory (11-XX) 120 Algebraic geometry (14-XX) 6 Commutative algebra (13-XX) 4 Dynamical systems and ergodic theory (37-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 \(K\)-theory (19-XX) 2 Quantum theory (81-XX) 2 Operations research, mathematical programming (90-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.