Nonvanishing of Dirichlet L-functions

TL;DR

This paper proves that for a significant proportion of primitive Dirichlet characters with large prime moduli, their associated L-functions do not vanish at the central point, contributing to understanding their nonvanishing properties.

Contribution

It establishes a nonvanishing result for at least 3/8 of primitive Dirichlet characters of large prime modulus, a new quantitative nonvanishing proportion.

Findings

At least 3/8 of such characters have nonzero central L-values.

Provides a lower bound on the nonvanishing proportion.

Advances understanding of the distribution of nonvanishing L-values.

Abstract

We show that for at least 3/8 of the primitive Dirichlet characters $\chi$ of large prime modulus, the central value $L(1/2,\chi)$ does not vanish.