Non-vanishing of Dirichlet L-functions at the central point

TL;DR

This paper introduces a novel mollifier technique to demonstrate that at least 34% of primitive Dirichlet L-functions do not vanish at the central point, advancing understanding of their non-vanishing properties.

Contribution

The paper presents a new two-piece mollifier method to improve non-vanishing results for Dirichlet L-functions at the central point.

Findings

Proves at least 34% of primitive Dirichlet L-functions are non-zero at s=1/2.

Introduces a novel two-piece mollifier technique.

Enhances previous non-vanishing proportion results.

Abstract

Let $\chi$ be a primitive Dirichlet character modulo $q$ and $L(s,\chi)$ be the Dirichlet L-function associated to $\chi$. Using a new two-piece mollifier we show that $L(\tfrac{1}{2},\chi)\ne0$ for at least 34% of the characters in the family.