William A. Stein References Cited

(617) 308-0144  was@math.harvard.edu  http://modular.fas.harvard.edu

References

[AS] A. Agashe and W. A. Stein, Visible Evidence for the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties of Analytic Rank 0, To appear in Math. of Computation.

[AS02] , Visibility of Shafarevich-Tate groups of abelian varieties, J. Number Theory 97 (2002), no. 1, 171–185. MR 2003h:11070

[BCDT01] C. Breuil, B. Conrad, F. Diamond, and R. Taylor, On the modularity of elliptic curves over Q: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843–939 (electronic). MR 2002d:11058

[BCP97] W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), no. 3-4, 235–265, Computational algebra and number theory (London, 1993). MR 1 484 478

[Bir71] B. J. Birch, Elliptic curves over Q: A progress report, 1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969), Amer. Math. Soc., Providence, R.I., 1971, pp. 396–400.

[CES03] B. Conrad, S. Edixhoven, and W. A. Stein, J_{1}(p) Has Connected Fibers, To appear in Documenta Mathematica (2003).

[Cre] J. E. Cremona, Elliptic curves of conductor ≤ 17000,

http://www.maths.nott.ac.uk/personal/jec/ftp/data/.

[CS02] B. Conrad and W. A. Stein, Component Groups of Purely Toric Quotients, To appear in Math Research Letters (2002).

[DWS] N. Dummigan, M. Watkins, and W. A. Stein, Constructing Elements in Shafarevich-Tate Groups of Modular Motives, To appear in “Number theory and algebraic geometry — to Peter Swinnerton-Dyer on his 75th birthday”, ed. by Miles Reid and Alexei Skorobogatov.

[Eme01] M. Emerton, Optimal Quotients of Modular Jacobians, preprint (2001).

[FpS^{+}01] E. V. Flynn, F. Leprévost, E. F. Schaefer, W. A. Stein, M. Stoll, and J. L. Wetherell, Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves, Math. Comp. 70 (2001), no. 236, 1675–1697 (electronic). MR 1 836 926

[Kat] K. Kato, p-adic Hodge theory and values of zeta functions of modular forms, Preprint, 244 pages.

William A. Stein References Cited

(617) 308-0144  was@math.harvard.edu  http://modular.fas.harvard.edu

[KL81] D. S. Kubert and S. Lang, Modular units, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 244, Springer-Verlag, New York, 1981. MR 84h:12009

[Lan91] S. Lang, Number theory. III, Springer-Verlag, Berlin, 1991, Diophantine geometry. MR 93a:11048

[Maz77] B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. (1977), no. 47, 33–186 (1978).

[Mer94] L. Merel, Universal Fourier expansions of modular forms, On Artin’s conjecture for odd 2-dimensional representations, Springer, 1994, pp. 59–94.

[Rib80] K. A. Ribet, Twists of modular forms and endomorphisms of abelian varieties, Math. Ann. 253 (1980), no. 1, 43–62. MR 82e:10043

[Rib90] , Raising the levels of modular representations, Séminaire de Théorie des Nombres, Paris 1987–88, Birkhäuser Boston, Boston, MA, 1990, pp. 259–271.

[Roh84] D. E. Rohrlich, On L-functions of elliptic curves and cyclotomic towers, Invent. Math. 75 (1984), no. 3, 409–423. MR 86g:11038b

[Rub98] K. Rubin, Euler systems and modular elliptic curves, Galois representations in arithmetic algebraic geometry (Durham, 1996), Cambridge Univ. Press, Cambridge, 1998, pp. 351–367. MR 2001a:11106

[Shi73] G. Shimura, On the factors of the jacobian variety of a modular function field, J. Math. Soc. Japan 25 (1973), no. 3, 523–544.

[Ste] W. A. Stein, Shafarevich-tate groups of nonsquare order, Proceedings of MCAV 2002, Progress of Mathematics (to appear).

[Ste03a] , The Modular Forms Database,

http://modular.fas.harvard.edu/Tables (2003).

[Ste03b] , Studying the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties Using MAGMA, To appear in J. Cannon, ed., Computational Experiments in Algebra and Geometry, Springer-Verlag (2003).

[Tat66] J. Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog, Séminaire Bourbaki, Vol. 9, Soc. Math. France, Paris, 1965/66, pp. Exp. No. 306, 415–440.