Spectral decomposition formula and moments of symmetric square L-functions

TL;DR

This paper establishes a spectral decomposition formula linking averages of Zagier L-series to moments of symmetric square L-functions for Maass and holomorphic cusp forms across various levels.

Contribution

It introduces a new spectral decomposition formula connecting Zagier L-series averages with symmetric square L-function moments for specific levels.

Findings

Derived a spectral decomposition formula for Zagier L-series averages.

Connected Zagier L-series with symmetric square L-function moments.

Applicable to Maass and holomorphic cusp forms at levels 4, 16, 64.

Abstract

We prove a spectral decomposition formula for averages of Zagier L-series in terms of moments of symmetric square L-functions associated to Maass and holomorphic cusp forms of levels 4, 16, 64.