On the Rankin-Selberg L-function related to the Godement-Jacquet L-function II

2023/09/01 by Kaur, Amrinder, Sankaranarayanan, Ayyadurai
#11F30 #11N75 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.00243

Abstract

In this paper, we consider the k-th Riesz mean for the coefficients of the Rankin-Selberg L-function L_{f × f}(s) related to the Godement-Jacquet L-function with respect to SL(n,ℤ). We establish an asymptotic formula for the k-th Riesz mean with an improved range and a better error term. As a result, we get an asymptotic relation for the partial sum of the coefficients of L_{f × f}(s).

Related

• The central value of the Rankin-Selberg L-functions
• Weight aspect asymptotic and simultaneous non-vanishing for Rankin-Selberg L-functions
• Cohomology classes, periods, and special values of Rankin-Selberg L-functions
• New integral representations for Rankin-Selberg L-functions
• Product of Rankin-Selberg convolutions and a new proof of Jacquet's local converse conjecture