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

2025/10/22 by Ghosh, Aritra
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.19468

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 \citeBH2) and getting a square root exponent for the error term.

Citations

• Simultaneous non-vanishing of central values of GL(2) × GL(3) and GL(3) L-functions
• A Spectral reciprocity formula and non-vanishing for L-functions on\n GL(4)xGL(2)
• Mollification and non-vanishing of automorphic L-functions on GL(3)
• Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions
• The central value of the Rankin-Selberg L-functions
• On Certain L-Functions

Related

• The central value of the Rankin-Selberg L-functions
• The Zero Density Theorem for the Rankin-Selberg L-function and its applications
• New integral representations for Rankin-Selberg L-functions
• Real zeros and size of Rankin-Selberg L-functions in the level aspect
• On the Rankin-Selberg L-function related to the Godement-Jacquet L-function II