The second moment of symmetric square L-functions over Gaussian integers

TL;DR

This paper establishes a new upper bound for the second moment of symmetric square L-functions over Gaussian integers, leading to improved error estimates in the prime geodesic theorem for the Picard manifold.

Contribution

It provides a novel upper bound on the second moment of symmetric square L-functions over Gaussian integers, enhancing previous results.

Findings

Improved upper bound on the second moment of L-functions.

Enhanced error term in the prime geodesic theorem.

Application to the Picard manifold's spectral analysis.

Abstract

We prove a new upper bound on the second moment of Maass form symmetric square L-functions defined over Gaussian integers. Combining this estimate with the recent result of Balog-Biro-Cherubini-Laaksonen, we improve the error term in the prime geodesic theorem for the Picard manifold.