An asymptotic formula of spectral average of central $L$-values on ${\bf GSp}(2)$ for square free levels
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910890881712128 |
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| author | Kuga, Seiji Tsuzuki, Masao |
| author_facet | Kuga, Seiji Tsuzuki, Masao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An asymptotic formula of spectral average of central $L$-values on ${\bf GSp}(2)$ for square free levels Kuga, Seiji Tsuzuki, Masao Number Theory 11F46, 11F67, 11F72 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. |
| title | An asymptotic formula of spectral average of central $L$-values on ${\bf GSp}(2)$ for square free levels |
| topic | Number Theory 11F46, 11F67, 11F72 |
| url | https://arxiv.org/abs/2410.03166 |