Nonvanishing of Dirichlet L-functions, II

TL;DR

This paper proves that at least 5/13 of primitive Dirichlet L-functions at the central point do not vanish for large prime moduli, improving previous bounds and advancing understanding of L-function nonvanishing.

Contribution

It improves the lower bound on the proportion of nonvanishing Dirichlet L-functions at the central point for large prime moduli.

Findings

At least 5/13 of primitive Dirichlet L-functions do not vanish at 1/2.

Improves previous nonvanishing proportion of 3/8.

Results hold for large prime moduli.

Abstract

We show that for at least $\frac{5}{13}$ of the primitive Dirichlet characters $\chi$ of large prime modulus, the central value $L(\frac{1}{2},\chi)$ does not vanish, improving on the previous best known result of $\frac{3}{8}$.