Ward, Thomas (2013) Non-vanishing of Artin-twisted L-functions of elliptic curves. Journal of the Ramanujan Mathematical Society, Volume 28 (Number 2). pp. 233-245. ISSN 2320-3110.

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Abstract

Let E be an elliptic curve and ρ an Artin representation, both defined over Q. Let p be a prime at which E has good reduction. We prove that there exists an infinite set of Dirichlet characters χ, ramified only at p, such that the Artin-twisted L-values L(E,ρ \otimes χ, β) are non-zero when β lies in a specified region in the critical strip (assuming the conjectural continuations and functional equations for these L-functions). The new contribution of our paper is that we may choose our characters to be ramified only at one prime, which may divide the conductor of ρ.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Curves, Elliptic, Curves, Algebraic, L-functions, Number theory
Journal or Publication Title:	Journal of the Ramanujan Mathematical Society
Publisher:	The Ramanujan Mathematical Society
ISSN:	2320-3110
Official Date:	13 June 2013
Dates:	Date Event 13 June 2013 Published
Volume:	Volume 28
Number:	Number 2
Page Range:	pp. 233-245
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	25 December 2015
Date of first compliant Open Access:	25 December 2015

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