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2011 Numerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture
Werner Bley
Experiment. Math. 20(4): 426-456 (2011).

Abstract

Let $E/ \mathbb{Q}$ be an elliptic curve and $K/ \mathbb{Q}$ a finite Galois extension with group $G$. We write $E_K$ for the base change of $E$ and consider the equivariant Tamagawa number conjecture for the pair $(h^1(E_K )(1), \mathbb{Z}[G])$. This conjecture is an equivariant refinement of the Birch and Swinnerton-Dyer conjecture for $E/K$. For almost all primes $l$, we derive an explicit formulation of the conjecture that makes it amenable to numerical verifications. We use this to provide convincing numerical evidence in favor of the conjecture.

Citation

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Werner Bley. "Numerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture." Experiment. Math. 20 (4) 426 - 456, 2011.

Information

Published: 2011
First available in Project Euclid: 8 December 2011

zbMATH: 1277.11072
MathSciNet: MR2859900

Subjects:
Primary: 11G05, 11G40, 14G10

Rights: Copyright © 2011 A K Peters, Ltd.

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Vol.20 • No. 4 • 2011
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