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

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

2012-02-10

arxiv.org/abs/1202.2320v3

Mathematics

Number Theory

9 pages

Scientific paper

Let E be an elliptic curve and \rho an Artin representation, both defined over the rational numbers. Let S be a finite set of primes, including a prime p at which E has good reduction. We prove that there exists an infinite set of Dirichlet characters \chi, unramified outside S, such that the Artin-twisted L-values L(E,\rho\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).

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