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Ward, Thomas
- Non-Vanishing of Artin-Twisted L-functions of Elliptic Curves
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1 Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, GB
1 Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, GB
Source
Journal of the Ramanujan Mathematical Society, Vol 28, No 2 (2013), Pagination: 233–245Abstract
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 ⊗ χ,β) are nonzero 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.