Lower bounds for moments of quadratic twists of modular $L$-functions

TL;DR

This paper proves precise lower bounds for the moments of quadratic twists of modular L-functions at the central point, advancing understanding of their distribution and size.

Contribution

It provides sharp lower bounds for the 2k-th moments of quadratic twists of modular L-functions for all k ≥ 1/2, a significant improvement in the field.

Findings

Established sharp lower bounds for moments at the central point.

Extended results to the range k ≥ 1/2.

Enhanced understanding of the size and distribution of quadratic twists.

Abstract

We establish sharp lower bounds for the $2k$-th moment in the range $k \geq 1/2$ of the family of quadratic twists of modular $L$-functions at the central point.