Vanishing and non-vanishing Dirichlet twists of L-functions of elliptic curves

摘要

Let L(E/,?s) be the L-function of an elliptic curve E defined over the rational field ?. We examine the vanishing and non-vanishing of the central values L(E, 1,χ) of the twisted L-function as ranges over Dirichlet characters of a given order.