Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture (Part II)
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- by Werner Bley;
- Math. Comp. 81 (2012), 1681-1705
- DOI: https://doi.org/10.1090/S0025-5718-2012-02572-5
- Published electronically: January 25, 2012
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Abstract:
We continue the study of the Equivariant Tamagawa Number Conjecture for the base change of an elliptic curve begun by the author in 2009. We recall that the methods developed there, apart from very special cases, cannot be applied to verify the $l$-part of the ETNC if $l$ divides the order of the group. In this note we focus on extensions of $l$-power degree ($l$ an odd prime) and describe methods for computing numerical evidence for ETNC${_l}$. For cyclic $l$-power extensions we also express the validity of ETNC${_l}$ in terms of explicit congruences.References
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Bibliographic Information
- Werner Bley
- Affiliation: Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
- Email: bley@math.lmu.de
- Received by editor(s): August 4, 2010
- Received by editor(s) in revised form: April 26, 2011
- Published electronically: January 25, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1681-1705
- MSC (2010): Primary 11G40, 14G10, 11G05
- DOI: https://doi.org/10.1090/S0025-5718-2012-02572-5
- MathSciNet review: 2904598