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arXiv · 2410.03166

An asymptotic formula of spectral average of central $L$-values on ${\bf GSp}(2)$ for square free levels

Seiji Kuga·Masao Tsuzuki
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Abstract

We develop a new kind of relative trace formulas on ${\bf PGSp}_2$ involving the Bessel periods and the Rankin-Selberg type integral a la Piatetski-Shapiro for Siegel cusp forms on its spectral side. As an application, a version of weighted equidistribution theorems for the Satake parameters of Siegel cusp forms of square-free level and of scalar weights is proved.

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Seiji Kuga, Masao Tsuzuki. 2024-10-04. An asymptotic formula of spectral average of central $L$-values on ${\bf GSp}(2)$ for square free levels. https://arxiv.org/abs/2410.03166

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