Central values of derivatives of Dirichlet L-functions

Abstract

Let C(q,+) be the set of even, primitive Dirichlet characters (mod q). Using the mollifier method we show that L^{(k)}(1/2,chi) is not equal to zero for almost all the characters chi in C(q,+) when k and q are large. Here, L^{(k)}(s,chi) is the k-th derivative of of the Dirichlet L-function L(s,chi).

submitted for publication

References in corpus (1)

• Mean values with cubic characters

Cited by in corpus (3)

• Shifted Euler constants and a generalization of Euler-Stieltjes constants
• One-level density estimates for Dirichlet L-functions with extended support
• Average non-vanishing of Dirichlet $L$-functions at the central point