An effective version of the Kuznetsov trace formula for GSp(4)
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909508408705024 |
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| author | Comtat, Félicien Lesesvre, Didier Man, Siu Hang |
| author_facet | Comtat, Félicien Lesesvre, Didier Man, Siu Hang |
| contents | We develop an explicit version of the Kuznetsov trace formula for GSp(4), relating sums of Fourier coefficients to Kloosterman sums. We study the precise analytic behaviour of both the spectral and the arithmetic transforms arising in the Kuznetsov trace formula for GSp(4). We use these results to provide an effective version of the trace formula, and establish various results on the family of Maaß automorphic forms on GSp(4) in the spectral aspect: the Weyl law, a density result on the non-tempered spectrum, large sieve inequalities, bounds on the second moment of the spinor and standard $L$-functions, as well as a statement on the distribution of the low-lying zeros of these $L$-functions, determining the associated types of symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An effective version of the Kuznetsov trace formula for GSp(4) Comtat, Félicien Lesesvre, Didier Man, Siu Hang Number Theory Representation Theory 11F30, 11F46, 11F77 We develop an explicit version of the Kuznetsov trace formula for GSp(4), relating sums of Fourier coefficients to Kloosterman sums. We study the precise analytic behaviour of both the spectral and the arithmetic transforms arising in the Kuznetsov trace formula for GSp(4). We use these results to provide an effective version of the trace formula, and establish various results on the family of Maaß automorphic forms on GSp(4) in the spectral aspect: the Weyl law, a density result on the non-tempered spectrum, large sieve inequalities, bounds on the second moment of the spinor and standard $L$-functions, as well as a statement on the distribution of the low-lying zeros of these $L$-functions, determining the associated types of symmetry. |
| title | An effective version of the Kuznetsov trace formula for GSp(4) |
| topic | Number Theory Representation Theory 11F30, 11F46, 11F77 |
| url | https://arxiv.org/abs/2502.17234 |