Moments of symmetric square L-functions on GL(3)

TL;DR

This paper derives an asymptotic formula for the first moment of symmetric square L-functions on GL(3) in the level aspect, supporting the random matrix model and providing non-vanishing results.

Contribution

It introduces a new asymptotic formula with power saving error term for the twisted first moment of symmetric square L-functions on GL(3), including detailed local computations.

Findings

Asymptotic formula with power saving error term

Non-vanishing results for symmetric square L-functions

Lower bounds supporting the random matrix model

Abstract

We give an asymptotic formula with power saving error term for the twisted first moment of symmetric square L-functions on GL(3) in the level aspect. As applications, we obtain non-vanishing results as well as lower bounds of the expected order of magnitude for all even moments, supporting the random matrix model for a unitary ensemble. Besides the GL(3) Kuznetsov formula, the ingredients include detailed local computations at ramified places, including root numbers and orthonormalization of oldforms and Eisenstein series.