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arXiv · 2006.03036

Symplectic Kloosterman Sums and Poincar\'e Series

Siu Hang Man
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Abstract

We prove power-saving bounds for general Kloosterman sums on $\operatorname{Sp}(4)$ associated to all Weyl elements via a stratification argument coupled with $p$-adic stationary phase methods. We relate these Kloosterman sums to the Fourier coefficients of $\operatorname{Sp}(4)$ Poincar\'e series.

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Siu Hang Man. 2020-06-04. Symplectic Kloosterman Sums and Poincar\'e Series. https://doi.org/10.1007/s11139-021-00498-5

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