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

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

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

Vanishing and Non-vanishing Dirichlet Twists of L-functions of Elliptic Curves Jack Fearnley, Hershy Kisilevsky, and Masato Kuwata

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

Non-vanishing of Quadratic Twists of Modular L-functions

Vanishing of L-functions of Elliptic Curves over Number Fields

Let E be an elliptic curve over Q, with L-function LE(s). For any primitive Dirichlet character χ, let LE(s, χ) be the L-function of E twisted by χ. In this paper, we use random matrix theory to study vanishing of the twisted L-functions LE(s, χ) at the central value s = 1. In particular, random matrix theory predicts that there are infinitely many characters of order 3 and 5 such that LE(1, χ)...

On the Vanishing of Twisted L-Functions of Elliptic Curves

Let E be an elliptic curve over Q with L-function LE(s). We use the random matrix model of Katz and Sarnak to develop a heuristic for the frequency of vanishing of the twisted L-functions LE(1, χ), as χ runs over the Dirichlet characters of order 3 (cubic twists). The heuristic suggests that the number of cubic twists of conductor less than X for which LE(1, χ) vanishes is asymptotic to bEX 1/2...