The sixth moment of automorphic $L$-functions

TL;DR

This paper establishes an asymptotic formula for the sixth moment of automorphic L-functions associated with eigenforms for the congruence subgroup Γ₁(q), advancing understanding of their value distribution.

Contribution

It provides the first asymptotic formula for the sixth moment of automorphic L-functions in this family, a significant step in analytic number theory.

Findings

Derived an asymptotic formula for the sixth moment

Enhanced understanding of automorphic L-function value distribution

Paved the way for future higher-moment studies

Abstract

In this paper, we consider the $L$-functions $L(s, f)$ where $f$ is an eigenform for the congruence subgroup $\Gamma_1(q)$. We prove an asymptotic formula for the sixth moment of this family of automorphic $L$-functions.