The sixth moment of automorphic $L$-functions

TL;DR

This paper studies the sixth moment of automorphic L-functions for holomorphic modular forms on GL_2, providing an improved, unconditional upper bound that matches the expected order of magnitude.

Contribution

It offers the first unconditional upper bound of the correct order for the sixth moment of these automorphic L-functions, advancing understanding in the field.

Findings

Unconditional upper bound of the sixth moment obtained

Bound matches the expected order of magnitude

Improves upon previous work in the area

Abstract

We investigate the sixth moment of the family of $L$-functions associated to holomorphic modular forms on $GL_2$ with respect to a congruence subgroup $\Gamma_1(q)$. We improve on previous work and obtain an unconditional upper bound of the correct order of magnitude.