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arXiv · 2507.09125

On a Generalization of Motohashi's Formula: Non-archimedean Weight Functions

Han Wu
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Abstract

This is a continuation of the adelic version of Kwan's formula. At non-archimedean places we give a bound of the weight function on the mixed moment side, when the weight function on the $\mathrm{PGL}_3 \times \mathrm{PGL}_2$ side is nearly the characteristic function of a short family. Our method works for any tempered representation $\Pi$ of $\mathrm{PGL}_3$, and reveals the structural reason for the appearance of Katz's hypergeometric sums in a previous joint work with P.Xi.

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Han Wu. 2025-07-12. On a Generalization of Motohashi's Formula: Non-archimedean Weight Functions. https://arxiv.org/abs/2507.09125

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