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arXiv · 2502.17234

An effective version of the Kuznetsov trace formula for GSp(4)

Félicien Comtat·Didier Lesesvre·Siu Hang Man
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Abstract

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.

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Félicien Comtat, Didier Lesesvre, Siu Hang Man. 2025-02-24. An effective version of the Kuznetsov trace formula for GSp(4). https://arxiv.org/abs/2502.17234

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