Lower bounds for negative moments of quadratic Dirichlet $L$-functions

TL;DR

This paper derives lower bounds for negative moments of quadratic Dirichlet L-functions at the central point, assuming Chowla's conjecture, extending understanding of their size distribution.

Contribution

It provides the first known lower bounds for all negative moments of quadratic Dirichlet L-functions at the central point under a key conjecture.

Findings

Established lower bounds for all negative moments with k<0

Results depend on Chowla's conjecture about non-vanishing

Advances the understanding of L-function value distribution

Abstract

We establish lower bounds for the $2k$-th moment of families of quadratic Dirichlet $L$-functions at the central point for all real $k<0$, assuming a conjecture of S. Chowla on the non-vanishing of these $L$-values.