Stable averages of central values of Rankin-Selberg L-functions: some new variants

TL;DR

This paper derives exact formulas for averages of Rankin-Selberg L-values, extending previous stable formulas to more general cases including prime power levels and real dihedral twists.

Contribution

It provides new exact finite formulas for twisted first moments of Rankin-Selberg L-values in broader settings than previously known.

Findings

Exact finite formulas for twisted first moments of L-values

Stable formulas extended to prime power levels

Results applicable to real dihedral twists

Abstract

As shown by Michel-Ramakrishan (2007) and later generalized by Feigon-Whitehouse (2008), there are "stable" formulas for the average central L-value of the Rankin-Selberg convolutions of some holomorphic forms of fixed even weight and large level against a fixed imaginary quadratic theta series. We obtain exact finite formulas for twisted first moments of Rankin-Selberg L-values in much greater generality and prove analogous "stable" formulas when one considers either arbitrary modular twists of large prime power level or real dihedral twists of odd type associated to a Hecke character of mixed signature.