Kloosterman sums on orthogonal groups

2024/10/27 by Catinca Mujdei, Mujdei, Catinca
Mathematics · #11L05 #11L07 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2410.20569

openalex publication_date 2024/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Kloosterman sums on the orthogonal groups SO_3,3 and SO_4,2, associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are bounded by a combination of methods from algebraic geometry and p-adic analysis.

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