The number of cuspidal representations over a function field and its behavior under base changes

2025/04/29 by Takuro Fukayama, Fukayama, Takuro
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.20564

openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective curve over a finite field \mathbbF_q, k be its function field, and G be a simply connected almost simple split group over \mathbbF_q. We also write G for its structure over k. We calculate the sum of multiplicities of all cuspidal representations of G satisfying a given condition assuming the conjectural trace formula. We also observe how the sum changes if we replace X by its base change X⊗_\mathbbF_q\mathbbF_q^m.

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