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Mixed moments of $\rm GL(2)$ and symmetric square $L$-functions
Published 13 Mar 2024 in math.NT | (2403.08324v2)
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.
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