Mixed moments of \rm GL(2) and symmetric square L-functions

2024/03/13 by Huang, Bingrong, Li, Liangxun
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2403.08324

Abstract

In this paper, we prove asymptotic formulas of mixed moments of \rm GL(2) and its symmetric square L-functions for both Hecke--Maass cusp forms and holomorphic Hecke eigenforms in short intervals. As an application, we prove quantitative simultaneous non-vanishing of central values of these L-functions.

Related

• Mixed moments of Hecke eigenforms and L-functions
• Bounds for moments of symmetric square L-functions
• The first moment of central values of symmetric square L-functions in the weight aspect
• Simultaneous non-vanishing of central values of GL(2) × GL(3) and GL(3) L-functions
• A zero-density estimate for L-functions associated with \rm GL(3) Hecke--Maass cusp forms