# zbMATH — the first resource for mathematics

## Stein, William A.

Compute Distance To:
 Author ID: stein.william-a Published as: Stein, William; Stein, William A. External Links: MGP · Wikidata · GND
 Documents Indexed: 44 Publications since 2000, including 3 Books Biographic References: 1 Publication
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#### Co-Authors

 6 single-authored 4 Agashe, Amod 4 Watkins, Mark James 3 Balakrishnan, Jennifer S. 3 Mazur, Barry 3 Ribet, Kenneth Alan 2 Conrad, Brian 2 Jetchev, Dimitar P. 1 Bektemirov, Baur 1 Buzzard, Kevin 1 Calegari, Frank 1 Çiperiani, Mirela 1 Coleman, Robert Frederick 1 Dummigan, Neil 1 Edixhoven, Bas 1 Flynn, Eugene Victor 1 Grigorov, Grigor 1 Ho, Wei 1 Jorza, Andrei 1 Kaplan, Nathan 1 Kohel, David R. 1 Lauter, Kristin Estella 1 Leprévost, Franck 1 Merel, Loïc 1 Müller, Jan Steffen 1 Patrikis, Stefan T. 1 Schaefer, Edward F. 1 Spicer, Simon 1 Stoll, Michael 1 Tarniţǎ, Corina E. 1 Tate, John Torrence jun. 1 Verrill, Helena A. 1 Weigandt, James
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#### Serials

 5 Mathematics of Computation 4 Documenta Mathematica 3 IMRN. International Mathematics Research Notices 2 Journal of Number Theory 2 LMS Journal of Computation and Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Pacific Journal of Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Mathematical Research Letters 1 Pure and Applied Mathematics Quarterly

#### Fields

 32 Number theory (11-XX) 5 Algebraic geometry (14-XX)

#### Citations contained in zbMATH

39 Publications have been cited 328 times in 272 Documents Cited by Year
Modular forms, a computational approach. With an appendix by Paul E. Gunnells. Zbl 1110.11015
Stein, William
2007
The Manin constant. (With an appendix by J. Cremona). Zbl 1109.11032
Agashe, Amod; Ribet, Kenneth; Stein, William A.
2006
SAGE: system for algebra and geometry experimentation. Zbl 1341.68315
Stein, William; Joyner, David
2005
Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032
Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark
2007
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
2001
Computation of $$p$$-adic heights and log convergence. Zbl 1135.11034
Mazur, Barry; Stein, William; Tate, John
2007
$$J_1(p)$$ has connected fibers. Zbl 1101.14311
Conrad, Brian; Edixhoven, Bas; Stein, William
2003
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
2009
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
2005
Component groups of purely toric quotients. Zbl 1081.11040
2001
Lectures on Serre’s conjectures. Zbl 1160.11327
Ribet, Kenneth A.; Stein, William A.
2001
Algorithms for the arithmetic of elliptic curves using Iwasawa theory. Zbl 1336.11047
Stein, William; Wuthrich, Christian
2013
The modular degree, congruence primes, and multiplicity one. Zbl 1276.11087
Agashe, Amod; Ribet, Kenneth A.; Stein, William A.
2012
Visibility of Shafarevich-Tate groups of abelian varieties. Zbl 1101.14055
Agashe, Amod; Stein, William
2002
Fast computation of Hermite normal forms of random integer matrices. Zbl 1206.15027
Pernet, Clément; Stein, William
2010
Elementary number theory. Primes, congruences, and secrets. A computational approach. Zbl 1155.11002
Stein, William
2009
A database of elliptic curves – first report. Zbl 1058.11036
Stein, William A.; Watkins, Mark
2002
Shafarevich-Tate groups of nonsquare order. Zbl 1080.11047
Stein, William A.
2004
Modular parametrizations of Neumann-Setzer elliptic curves. Zbl 1088.11043
Stein, William; Watkins, Mark
2004
There are genus one curves over $${\mathbb Q}$$ of every odd index. Zbl 1002.11050
Stein, William A.
2002
The field generated by the points of small prime order on an elliptic curve. Zbl 1027.11041
Merel, Loïc; Stein, William A.
2001
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.
2016
Sage: creating a viable free open source alternative to Magma, Maple, Mathematica, and MATLAB. Zbl 1316.65123
Stein, William
2013
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
2008
Conjectures about discriminants of Hecke algebras of prime level. Zbl 1125.11320
Calegari, Frank; Stein, William A.
2004
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
2016
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
2013
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
2010
Explicit Heegner points: Kolyvagin’s conjecture and non-trivial elements in the Shafarevich-Tate group. Zbl 1228.11082
Jetchev, Dimitar; Lauter, Kristin; Stein, William
2009
An introduction to computing modular forms using modular symbols. Zbl 1188.11074
Stein, William A.
2008
Approximation of eigenforms of infinite slope by eigenforms of finite slope. Zbl 1101.11015
Coleman, Robert F.; Stein, William A.
2004
Constructing elements in Shafarevich-Tate groups of modular motives. Zbl 1161.11354
Dummigan, Neil; Stein, William; Watkins, Mark
2003
A mod five approach to modularity of icosahedral Galois representations. Zbl 1054.11028
Buzzard, Kevin; Stein, William A.
2002
Cuspidal modular symbols are transportable. Zbl 1049.11054
Stein, William A.; Verrill, Helena A.
2001
Component groups of quotients of $$J_0(N)$$. Zbl 0984.11022
Kohel, David R.; Stein, William A.
2000
Prime numbers and the Riemann hypothesis. Zbl 1356.11001
Mazur, Barry; Stein, William
2016
$$p$$-adic heights of Heegner points and $$\Lambda$$-adic regulators. Zbl 1316.11116
Balakrishnan, Jennifer S.; Çiperiani, Mirela; Stein, William
2015
Heegner points and the arithmetic of elliptic curves over ring class extensions. Zbl 1276.11088
2012
Toward a generalization of the Gross-Zagier conjecture. Zbl 1278.11070
Stein, William A.
2011
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.
2016
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
2016
Prime numbers and the Riemann hypothesis. Zbl 1356.11001
Mazur, Barry; Stein, William
2016
$$p$$-adic heights of Heegner points and $$\Lambda$$-adic regulators. Zbl 1316.11116
Balakrishnan, Jennifer S.; Çiperiani, Mirela; Stein, William
2015
Algorithms for the arithmetic of elliptic curves using Iwasawa theory. Zbl 1336.11047
Stein, William; Wuthrich, Christian
2013
Sage: creating a viable free open source alternative to Magma, Maple, Mathematica, and MATLAB. Zbl 1316.65123
Stein, William
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
2013
The modular degree, congruence primes, and multiplicity one. Zbl 1276.11087
Agashe, Amod; Ribet, Kenneth A.; Stein, William A.
2012
Heegner points and the arithmetic of elliptic curves over ring class extensions. Zbl 1276.11088
2012
Toward a generalization of the Gross-Zagier conjecture. Zbl 1278.11070
Stein, William A.
2011
Fast computation of Hermite normal forms of random integer matrices. Zbl 1206.15027
Pernet, Clément; Stein, William
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
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
2009
Elementary number theory. Primes, congruences, and secrets. A computational approach. Zbl 1155.11002
Stein, William
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
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
2008
An introduction to computing modular forms using modular symbols. Zbl 1188.11074
Stein, William A.
2008
Modular forms, a computational approach. With an appendix by Paul E. Gunnells. Zbl 1110.11015
Stein, William
2007
Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032
Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark
2007
Computation of $$p$$-adic heights and log convergence. Zbl 1135.11034
Mazur, Barry; Stein, William; Tate, John
2007
The Manin constant. (With an appendix by J. Cremona). Zbl 1109.11032
Agashe, Amod; Ribet, Kenneth; Stein, William A.
2006
SAGE: system for algebra and geometry experimentation. Zbl 1341.68315
Stein, William; Joyner, David
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
2005
Shafarevich-Tate groups of nonsquare order. Zbl 1080.11047
Stein, William A.
2004
Modular parametrizations of Neumann-Setzer elliptic curves. Zbl 1088.11043
Stein, William; Watkins, Mark
2004
Conjectures about discriminants of Hecke algebras of prime level. Zbl 1125.11320
Calegari, Frank; Stein, William A.
2004
Approximation of eigenforms of infinite slope by eigenforms of finite slope. Zbl 1101.11015
Coleman, Robert F.; Stein, William A.
2004
$$J_1(p)$$ has connected fibers. Zbl 1101.14311
Conrad, Brian; Edixhoven, Bas; Stein, William
2003
Constructing elements in Shafarevich-Tate groups of modular motives. Zbl 1161.11354
Dummigan, Neil; Stein, William; Watkins, Mark
2003
Visibility of Shafarevich-Tate groups of abelian varieties. Zbl 1101.14055
Agashe, Amod; Stein, William
2002
A database of elliptic curves – first report. Zbl 1058.11036
Stein, William A.; Watkins, Mark
2002
There are genus one curves over $${\mathbb Q}$$ of every odd index. Zbl 1002.11050
Stein, William A.
2002
A mod five approach to modularity of icosahedral Galois representations. Zbl 1054.11028
Buzzard, Kevin; Stein, William A.
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
2001
Component groups of purely toric quotients. Zbl 1081.11040
2001
Lectures on Serre’s conjectures. Zbl 1160.11327
Ribet, Kenneth A.; Stein, William A.
2001
The field generated by the points of small prime order on an elliptic curve. Zbl 1027.11041
Merel, Loïc; Stein, William A.
2001
Cuspidal modular symbols are transportable. Zbl 1049.11054
Stein, William A.; Verrill, Helena A.
2001
Component groups of quotients of $$J_0(N)$$. Zbl 0984.11022
Kohel, David R.; Stein, William A.
2000
all top 5

#### Cited by 382 Authors

 11 Stein, William A. 9 Balakrishnan, Jennifer S. 6 Agashe, Amod 6 Alaca, Ayşe 6 Mazur, Barry 6 Wuthrich, Christian 5 Alaca, Şaban 5 Aygin, Zafer Selçuk 5 Müller, Jan Steffen 5 Papikian, Mihran 5 Stoll, Michael 4 Fisher, Tom A. 4 Hutz, Benjamin 4 Siksek, Samir 3 Calegari, Frank 3 Gunnells, Paul E. 3 Hohenegger, Stefan 3 Lorenzini, Dino J. 3 Lozano-Robledo, Álvaro 3 Park, Yoon Kyung 3 Sahu, Brundaban 3 Shankar, Arul 3 Ye, Dongxi 2 Aguilera-Venegas, Gabriel 2 Ahlgren, Scott D. 2 Bennett, Michael A. 2 Besser, Amnon 2 Bhargava, Manjul 2 Braun, Oliver 2 Bruin, Nils 2 Bruin, Peter 2 Çeken, Seçil 2 Coulangeon, Renaud 2 Derickx, Maarten 2 Dixon, Lance J. 2 Dogra, Netan 2 Flynn, Eugene Victor 2 Galán-García, José Luis 2 Galán-García, María-Ángeles 2 Guitart, Xavier 2 Halle, Lars Halvard 2 Harvey, David I. 2 Ho, Wei 2 Jenkins, Paul M. 2 Jorza, Andrei 2 Kazalicki, Matija 2 Kesicioğlu, Yavuz 2 Kilford, Lloyd James Peter 2 Kim, Chan-Ho 2 Kirst, Peter 2 Kohen, Daniel 2 Krishna, K. Gopala 2 Lauder, Alan G. B. 2 Loeffler, David 2 Mascot, Nicolas 2 Masdeu, Marc 2 McLeod, Andrew J. 2 Miller, Robert L. 2 Palmieri, John H. 2 Papathanasiou, Georgios 2 Pernet, Clément 2 Poonen, Bjorn 2 Ramakrishnan, Balakrishnan 2 Rechnitzer, Andrew Daniel 2 Roberts, David Peter 2 Rodríguez-Cielos, Pedro 2 Rotger, Victor 2 Rubin, Karl Cooper 2 Schaefer, Edward F. 2 Silverberg, Alice 2 Singh, Anup Kumar 2 Sprung, Florian E. Ito 2 Stein, Oliver 2 Sun, Hae-Sang 2 Sutherland, Andrew V. 2 van Bommel, Raymond 2 Vigni, Stefano 2 Voight, John Michael 2 Volpato, Roberto 2 Vonk, Jan 2 Wang, Yanhua 2 Wewers, Stefan 2 Yasaki, Dan 2 Zhang, James J. 2 Zhang, Yichao 1 Agarwal, Mahesh 1 Altiary, Mada 1 Angelantonj, Carlo 1 Anni, Samuele 1 Ansmann, Gerrit 1 Armana, Cécile 1 Ash, Avner 1 Ashrafi, Ali Reza 1 Atencia-Mc. Killop, Iván 1 Baig, Salman 1 Bakker, Benjamin 1 Bannai, Eiichi 1 Barcau, Mugurel A. 1 Bastian, Brice 1 Bektemirov, Baur ...and 282 more Authors
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#### Cited in 75 Serials

 36 Journal of Number Theory 29 Mathematics of Computation 14 International Journal of Number Theory 11 Journal of High Energy Physics 10 Proceedings of the American Mathematical Society 10 Journal de Théorie des Nombres de Bordeaux 9 The Ramanujan Journal 8 LMS Journal of Computation and Mathematics 7 Journal of Algebra 6 Mathematische Annalen 5 Annales de l’Institut Fourier 5 Functiones et Approximatio. Commentarii Mathematici 5 Journal für die Reine und Angewandte Mathematik 5 Mathematische Zeitschrift 5 Transactions of the American Mathematical Society 5 Annals of Mathematics. Second Series 4 Inventiones Mathematicae 4 Bulletin of the American Mathematical Society. New Series 4 Experimental Mathematics 3 Acta Arithmetica 3 Advances in Mathematics 3 Compositio Mathematica 3 Duke Mathematical Journal 3 Journal of the Mathematical Society of Japan 3 Journal of Symbolic Computation 3 Linear Algebra and its Applications 3 Research in Number Theory 2 Israel Journal of Mathematics 2 Applied Mathematics and Computation 2 Manuscripta Mathematica 2 Theoretical Computer Science 2 Integers 2 Research in the Mathematical Sciences 2 SIAM Journal on Applied Algebra and Geometry 1 Computers & Mathematics with Applications 1 Discrete Applied Mathematics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Mathematische Semesterberichte 1 The Mathematical Intelligencer 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Statistics 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Geometriae Dedicata 1 Glasgow Mathematical Journal 1 Indiana University Mathematics Journal 1 Journal of Optimization Theory and Applications 1 Journal of Pure and Applied Algebra 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 European Journal of Combinatorics 1 Revista Matemática Iberoamericana 1 Formal Aspects of Computing 1 Journal of Global Optimization 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Geometry 1 Selecta Mathematica. New Series 1 Annals of Combinatorics 1 Chaos 1 Journal of the European Mathematical Society (JEMS) 1 Communications of the Korean Mathematical Society 1 Foundations of Computational Mathematics 1 Applied Mathematics E-Notes 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Central European Journal of Mathematics 1 Journal of Algebra and its Applications 1 Journal of Mathematical Cryptology 1 Algebra & Number Theory 1 Forum of Mathematics, Sigma 1 European Journal of Mathematics 1 Open Mathematics 1 Journal de l’École Polytechnique – Mathématiques
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#### Cited in 37 Fields

 228 Number theory (11-XX) 70 Algebraic geometry (14-XX) 10 Quantum theory (81-XX) 8 Relativity and gravitational theory (83-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Computer science (68-XX) 6 Combinatorics (05-XX) 6 Information and communication theory, circuits (94-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Numerical analysis (65-XX) 4 Nonassociative rings and algebras (17-XX) 4 Group theory and generalizations (20-XX) 3 Commutative algebra (13-XX) 3 Associative rings and algebras (16-XX) 2 Mathematical logic and foundations (03-XX) 2 Partial differential equations (35-XX) 2 Convex and discrete geometry (52-XX) 2 Manifolds and cell complexes (57-XX) 2 Fluid mechanics (76-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 $$K$$-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX)

#### Wikidata Timeline

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