Lower bounds for small fractional moments of Dirichlet $L$-functions

TL;DR

This paper establishes lower bounds for small rational moments of Dirichlet L-functions, revealing new techniques and implications for non-vanishing results at the critical line.

Contribution

It provides the first correct order lower bounds for small rational moments of Dirichlet L-functions, advancing understanding of their behavior in the conductor aspect.

Findings

Established lower bounds of correct order for small rational moments

Linked bounds to non-vanishing results at the critical line

Developed new techniques for analyzing L-function moments

Abstract

We prove a lower bound of the correct order of magnitude in the conductor aspect for small rational moments of Drichlet $L$-functions. Such bounds require new techniques, which is visible from the relationship to non-vanishing results for $L(1/2, \chi)$.