Asymptotics of a Gauss hypergeometric function related to moments of symmetric square L-functions I

TL;DR

This paper derives an asymptotic formula for a Gauss hypergeometric function linked to moments of symmetric square L-functions of Maass forms, aiding in establishing hybrid subconvexity bounds.

Contribution

It provides a uniform asymptotic formula for a specific hypergeometric function related to L-function moments, crucial for subconvexity bounds.

Findings

Established an asymptotic formula for the hypergeometric function

The formula is uniform across multiple variables

Facilitates proof of hybrid subconvexity bounds

Abstract

We prove an asymptotic formula for a special case of the Gauss hypergeometric function which arises in explicit formulas for moments of Maass form symmetric square L-functions. The resulting formula is uniform in several variables, which is crucial for proving hybrid subconvexity bounds for the L-functions under consideration.