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

Bouganis, A.; Dokchitser, V.

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
• Public URL: https://durham-repository.worktribe.com/output/1446160