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Algebraicity of L-values for elliptic curves in a false Tate curve tower

Published online by Cambridge University Press:  10 April 2007

THANASIS BOUGANIS  and
VLADIMIR DOKCHITSER
THANASIS BOUGANIS
Affiliation:
Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 288, D-69129 Heidelberg, Germany e-mail: [email protected]
VLADIMIR DOKCHITSER
Affiliation:
D.P.M.MS., University of Cambridge, Wilberforce Road, Cambridge CB3 OWB. e-mail: [email protected]
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Abstract

Let E be an elliptic curve over , and τ an Artin representation over that factors through the non-abelian extension , where p is an odd prime and n, m are positive integers. We show that L(E,τ,1), the special value at s=1 of the L-function of the twist of E by τ, divided by the classical transcendental period Ω+d+|Ω−d−|ε(τ) is algebraic and Galois-equivariant, as predicted by Deligne's conjecture.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 193 - 204
Copyright
Copyright © Cambridge Philosophical Society 2007

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