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

Title data

Balakrishnan, Jennifer S. ; Müller, Jan Steffen ; Stein, William A.:
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties.
In: Mathematics of Computation. Vol. 85 (March 2016) Issue 298 . - pp. 983-1016.
ISSN 0025-5718
DOI: https://doi.org/10.1090/mcom/3029

Project information

Project title:
Project's official titleProject's id
No informationSTO 299/5-1
No informationKU 2359/2-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

Mazur, Tate, and Teitelbaum gave a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for elliptic curves. We provide a generalization of their conjecture in the good ordinary case to higher dimensional modular abelian varieties over the rationals by constructing the p-adic L-function of a modular abelian variety and showing that it satisfies the appropriate interpolation property. This relies on a careful normalization of the padic L-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.

Further data

Item Type: Article in a journal
Refereed: Yes
Subject classification: 2010 Mathematics Subject Classification: Primary 11G40, 11G50, 11G10, 11G18
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 May 2017 10:57
Last Modified: 04 May 2017 10:57
URI: https://eref.uni-bayreuth.de/id/eprint/36944