Weight aspect asymptotic and simultaneous non-vanishing for Rankin-Selberg $L$-functions

TL;DR

This paper proves simultaneous non-vanishing of two Rankin-Selberg L-functions in the weight aspect by refining asymptotic estimates and removing t-integral dependence, leading to improved error bounds.

Contribution

It introduces a method to eliminate t-integral dependence in asymptotic results for Rankin-Selberg L-functions, achieving a square root error term exponent.

Findings

Established simultaneous non-vanishing in weight aspect

Improved error term to square root exponent

Extended previous results by removing t-dependence

Abstract

In this article we show simultaneous non-vanishing of two Rankin-Selberg $L$-functions by proving an asymptotic result in weight aspect. The main input of this paper is to remove the $t$-integral dependence from the result of Blomer-Harcos (see \cite{BH2}) and getting a square root exponent for the error term.