The Second Moment of Rankin-Selberg $L$-Functions in Conductor-Dropping Regimes

TL;DR

This paper derives an asymptotic formula for the second moment of Rankin-Selberg $L$-functions in cases where the conductor drops, focusing on holomorphic cusp forms of equal weight.

Contribution

It provides a new asymptotic formula for the second moment of Rankin-Selberg $L$-functions in conductor-dropping regimes for holomorphic cusp forms.

Findings

Established an asymptotic formula for the second moment.

Focused on cases with conductor dropping.

Applied to Rankin-Selberg convolutions of holomorphic cusp forms.

Abstract

We prove an asymptotic formula for the second moment of $L$-functions associated to the Rankin-Selberg convolution of two holomorphic Hecke cusp forms with equal weight.