Period integrals and Rankin-Selberg L-functions on GL(n)

TL;DR

This paper computes the second moment of Rankin-Selberg L-functions for GL(n), achieving bounds matching the Lindelöf hypothesis on average and recovering the convexity bound, with novel results even for n=2.

Contribution

It provides the first second moment calculation for these L-functions on GL(n), establishing bounds as strong as Lindelöf hypothesis on average.

Findings

Bound matches Lindelöf hypothesis on average

Recovers convexity bound individually

First such result for GL(n) L-functions

Abstract

We compute the second moment of a certain family of Rankin-Selberg $L$-functions L(f x g, 1/2) where f and g are Hecke-Maass cusp forms on GL(n). Our bound is as strong as the Lindel\"of hypothesis on average, and recovers individually the convexity bound. This result is new even in the classical case n=2.