Nonvanishing of quadratic Dirichlet L-functions at s=1/2

TL;DR

This paper proves that a positive proportion of quadratic Dirichlet L-functions do not vanish at the critical point s=1/2, advancing understanding of their nonvanishing behavior.

Contribution

It establishes that a positive proportion of fundamental discriminants have nonzero L-values at s=1/2, a significant result in analytic number theory.

Findings

A positive proportion of L(1/2, chi_d) are nonzero.

Supports conjectures about nonvanishing of L-functions.

Contributes to understanding of quadratic Dirichlet L-functions.

Abstract

We show that for a positive proportion of fundamental discriminants d, L(1/2,chi_d) != 0. Here chi_d is the primitive quadratic Dirichlet character of conductor d.