Non-vanishing of Artin-twisted L-functions of Elliptic Curves

Abstract

Let E be an elliptic curve and ρan Artin representation, both defined over the rational numbers. 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,ρχ,β) are non-zero when βlies 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.

arXiv comment11 pages

References in corpus (1)

• The GL_2 main conjecture for elliptic curves without complex multiplication

Cited by in corpus (1)

• Determination of elliptic curves by their adjoint $p$-adic $L$-functions