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

Bouganis, A.; Dokchitser, V.

doi:10.1017/s030500410600987x

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

Bouganis, A.; Dokchitser, V.

Authors

Professor Athanasios Bouganis athanasios.bouganis@durham.ac.uk
Professor

V. Dokchitser

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.

Citation

Bouganis, A., & Dokchitser, V. (2007). Algebraicity of L-values for elliptic curves in a false Tate curve tower. Mathematical Proceedings of the Cambridge Philosophical Society, 142(2), 193-204. https://doi.org/10.1017/s030500410600987x

Journal Article Type	Article
Online Publication Date	Apr 10, 2007
Publication Date	Apr 10, 2007
Deposit Date	Oct 4, 2013
Publicly Available Date	Apr 11, 2017
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Print ISSN	0305-0041
Electronic ISSN	1469-8064
Publisher	Cambridge University Press
Peer Reviewed	Peer Reviewed
Volume	142
Issue	2
Pages	193-204
DOI	https://doi.org/10.1017/s030500410600987x

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Copyright Statement
This article has been published in a revised form in Mathematical proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/S030500410600987X. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge Philosophical Society 2007