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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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On the Birch and Swinnerton-Dyer formula for quotients of J0(N)
by
Amod Agashe
University of California, Berkeley
Coauthors: William Stein

We investigate the Birch and Swinnerton-Dyer conjectural formula for certain quotients of J0(N). This formula relates relates the special L-value to certain arithmetic invariants of the quotient. We prove formulae for calculating the terms in the formula and present some computations. Finally we shall indicate how one can try to use congruences to give a lower bound on the order of the Tate-Shafarevich group, and thus hope to make progress towards proving the Birch and Swinnerton-Dyer conjectural formula.

http://www.math.berkeley.edu/~amod

Date received: March 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-69.