Mixed integral moments of the Hecke $L$-functions and Riemann zeta function

TL;DR

This paper derives an asymptotic formula for the mixed moments of the Riemann zeta function squared and Hecke L-functions on the critical line, applicable to both holomorphic and Maass forms.

Contribution

It provides a new asymptotic formula for mixed moments involving the Riemann zeta function and Hecke L-functions, extending previous results to a broader class of automorphic forms.

Findings

Established an asymptotic formula for mixed moments on the critical line.

Applicable to both holomorphic and Maass forms.

Advances understanding of the correlation between zeta and L-functions.

Abstract

In this paper, let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We establish an asymptotic formula for the mixed moment of $\zeta^{2}(s)$ and $L(s,f)$ on the critical line, valid for both holomorphic and Maass forms.