Non-vanishing of Dirichlet $L$-functions with smooth conductors

TL;DR

This paper proves that for large, smooth, square-free conductors, at least 35.9% of primitive Dirichlet L-functions do not vanish at the central point, advancing understanding of their distribution.

Contribution

It establishes a quantitative non-vanishing result for Dirichlet L-functions with smooth conductors, a novel achievement in analytic number theory.

Findings

At least 35.9% of such L-functions are non-zero at the center.

The result applies to large, square-free, smooth conductors.

Provides new insights into the distribution of zeros of Dirichlet L-functions.

Abstract

Given a large, square-free, smooth conductor, we establish the non-vanishing of the central values for at least $35.9\%$ of the primitive Dirichlet $L$-functions.