Publications

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William A. Stein

My publications are listed below; many have been published or at least accepted for publication, and each is available here. You might also want to look at some of my rougher papers, notes for somes talks, and my journal copyright gossip page.
Download MathSciNet reviews of all my papers: PDF, DVI, or HTML.
  1. Verification of the Birch and Swinnerton-Dyer Conjecture for Specific Elliptic Curves, with G. Grigorov, A. Jorza, S. Patrikis, and C. Patrascu (26 pages)
  2. Visualizing Elements of Shafarevich-Tate Groups at Higher Level, with Dimitar Jetchev (28 pages)
  3. What Do Modular Forms Attached to Elliptic Curves Look Like?, with K. Grosvenor (7 pages)
  4. Visibility of Mordell-Weil Groups (20 pages)
  5. Elementary Number Theory (181 page book)
  6. A Brief Introduction To Classical and Adelic Algebraic Number Theory (190 page book).
  7. Conjectures About Discriminants of Hecke Algebras of Prime Level, with Frank Calegari (ANTS VI Proceedings, 2004).
  8. Modular Degrees of Neumann-Setzer Curves, with Mark Watkins (IMRN 2004, no 27, 1395-1405).
  9. The Manin Constant, Congruence Primes, and the Modular Degree, with Amod Agashe (preprint).
  10. Studying the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties Using MAGMA (to appear as a chapter in a book for Springer-Verlag edited by John Cannon).
  11. A Database of Elliptic Curves---First Report, with Mark Watkins (ANTS V proceedings, Sydney, Australia, 2002).
  12. Constructing Elements in Shafarevich-Tate Groups of Modular Motives, with Neil Dummigan and Mark Watkins ("Number theory and algebraic geometry--to Peter Swinnerton-Dyer on his 75th birthday", Ed. M. Reid and A. Skorobogatov, pages 91-118).
  13. Shafarevich-Tate Groups of Nonsquare Order (Progress in Math., 224 (2004), 277-289, Birkhauser).
  14. Approximation of Infinite-Slope Modular Eigenforms By Finite-Slope Eigenforms, with Robert Coleman (Dwork Proceedings).
  15. J1(p) Has Connected Fibers, with Brian Conrad and Bas Edixhoven (Documenta Mathematica, 8 (2003), pages 331-408).
  16. Visible Evidence for the Birch and Swinnerton-Dyer Conjecture for Rank 0 Modular Abelian Varieties, with Amod Agashe, and an appendix by Mazur and Cremona (in Math. Comp., Vol 74, Number 249, pages 455-484).
  17. Visibility of Shafarevich-Tate Groups of Abelian Varieties, with Amod Agashe (J. of Number Theory, 97 (2002), no. 1, 171-185.)
  18. Component Groups of Purely Toric Quotients of Semistable Jacobians, with Brian Conrad (Math. Res. Letters, 8 (2001) no. 5-6, 745-766)
  19. Appendix on Generating the Hecke Algebra, with Amod Agashe (Experimental Math., 11 (2002), no. 2, 303-311).
  20. The field generated by the points of small prime order on an elliptic curve, with Loic Merel (IMRN, 2001, no. 20, 1075-1082.)
  21. An introduction to computing modular forms using modular symbols (to appear in an MSRI proceedings).
  22. Lectures on Serre's conjectures, with Ken Ribet (Arithmetic Algebraic Geometry, IAS/Park City Math. Inst. Series, Vol. 9, 143-232).
  23. Cuspidal modular symbols are transportable, with Helena Verrill (LMS Journal of Computation and Mathematics, 4 (2001), 170-181).
  24. There are genus one curves over Q of every odd index (J. Reine Angew. Math. 547 (2002), 139-147).
  25. A mod five approach to modularity of icosahedral Galois representations, with Kevin Buzzard (Pac. J. Math. 203 (2002), no. 2, 265-282)
  26. Explicit approaches to modular abelian varieties (UC Berkeley Ph.D. thesis)
  27. Component groups of quotients of J0(N), with David Kohel (ANTS IV proceedings)
  28. Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves, with five coauthors (Mathematics of Computation, 70 (2001), no . 236, 1675-1697).