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arXiv · 2512.16680

Symplectic Kloosterman Sums for $\operatorname{Sp}(2n)$ with Powerful Moduli

Gilles Felber
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Abstract

We prove a non-trivial bound for $\operatorname{Sp}(2n)$ Kloosterman sums of moduli not equal to a prime multiple of the identity. These sums are attached to Siegel modular forms on the group $\operatorname{Sp}(2n)$ and appear in the corresponding Petersson formula. We give an application to equidistribution of coprime symmetric pairs.

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Gilles Felber. 2025-12-18. Symplectic Kloosterman Sums for $\operatorname{Sp}(2n)$ with Powerful Moduli. https://arxiv.org/abs/2512.16680

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