A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties

-function, which we achieve by a comparison of periods. Our generalization agrees with the conjecture of Mazur, Tate, and Teitelbaum in dimension 1 and the classical Birch and Swinnerton-Dyer conjecture formulated by Tate in rank 0. We describe the theoretical techniques used to formulate the conjec...

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Bibliographic Details
Published in:Mathematics of computation 2016-03, Vol.85 (298), p.983-1016
Main Authors: Balakrishnan, Jennifer S., Müller, J. Steffen, Stein, William A.
Format: Article
Language:English
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Summary:-function, which we achieve by a comparison of periods. Our generalization agrees with the conjecture of Mazur, Tate, and Teitelbaum in dimension 1 and the classical Birch and Swinnerton-Dyer conjecture formulated by Tate in rank 0. We describe the theoretical techniques used to formulate the conjecture and give numerical evidence supporting the conjecture in the case when the modular abelian variety is of dimension 2.]]>
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/3029