The second moment of Maass form symmetric square L-functions at the central point

TL;DR

This paper offers an alternative proof for the mean Lindel"{o}f estimate of the second moment of symmetric-square Maass form L-functions at the central point, extending understanding of their value distribution.

Contribution

It provides a new proof of an existing mean Lindel"{o}f estimate for the second moment of symmetric-square Maass form L-functions at the central point.

Findings

Confirmed the mean Lindel"{o}f estimate for the second moment.

Extended the interval for spectral parameters in the estimate.

Provided methodological improvements over previous proofs.

Abstract

Recently R.Khan and M.Young proved a mean Lindel\"{o}f estimate on the second moment of central values of Maass form symmetric-square $L$-function on the interval $T<|t_j|<T+T^{1/5+\epsilon}$, where $t_j$ is a spectral parameter of the Maass form. We provide another proof of this result.