科研之友
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摘要
Let E be an elliptic curve and rho 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 chi, ramified only at p, such that the Artin-twisted L-values L(E, rho circle times chi, beta) are non-zero when beta 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 rho.
- 出版日期2013-6
