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Mathematics of Computation

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Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture (Part II)

Author: Werner Bley
Journal: Math. Comp. 81 (2012), 1681-1705
MSC (2010): Primary 11G40, 14G10, 11G05
Published electronically: January 25, 2012
MathSciNet review: 2904598
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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.

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Werner Bley
Affiliation: Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany

Received by editor(s): August 4, 2010
Received by editor(s) in revised form: April 26, 2011
Published electronically: January 25, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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