A hybrid asymptotic formula for the second moment of Rankin-Selberg L-functions

TL;DR

This paper derives an asymptotic formula with a power-saving error term for the second moment of Rankin-Selberg L-functions, focusing on families of modular forms with specific fixed parameters, and also addresses the fourth moment in special cases.

Contribution

It introduces a hybrid asymptotic formula for the second moment of Rankin-Selberg L-functions, extending previous results to more general ranges and including a special case for the fourth moment.

Findings

Derived an asymptotic formula with power-saving error term

Extended analysis to a broader range of parameters

Provided results for the fourth moment of L-functions

Abstract

We consider the Rankin-Selberg L-functions associated with a fixed modular form of full level and holomorphic cuspidal newforms of large even weight, fixed level and fixed primitive nebentypus. We compute the second moment of this family in fairly general ranges, and obtain an asymptotic formula with a power saving error term. A special case treats the fourth moment of L-functions associated with holomorphic cusp forms.