A uniform Weyl bound for L-functions of Hilbert modular forms

2023/02/28 by Han Wu, Wu, Han, Ping Xi +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.14652

openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a Weyl-type subconvexity of L(\tfrac12,f) for spherical Hilbert newforms f with level ideal \mathfrakN², in which \mathfrakN is required to be cube-free, and at any prime ideal \mathfrakp with \mathfrakp² | \mathfrakN the local representation generated by f is not supercuspidal. The proof exploits a distributional version of Motohashi's formula over number fields developed by the first author, as well as Katz's work on hypergeometric sums over finite fields in the language of ℓ-adic cohomology.

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

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