On equidistribution of Gauss sums of cuspidal representations of GL_d(\mathbb F_q)

2021/10/06 by Sameer Kulkarni, Kulkarni, Sameer, C. S. Rajan +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.02741

openalex publication_date 2021/10/06 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

We investigate the distribution of the angles of Gauss sums attached to the cuspidal representations of general linear groups over finite fields. In particular we show that they happen to be equidistributed w.r.t.the Haar measure. However, for representations of PGL₂(\mathbb F_q), they are clustered around 1 and -1 for odd p and around 1 for p=2.

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