On equidistribution of Gauss sums of cuspidal representations of $G{L}_d({\mathbb{F}}_q)$

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 $PG{L}_2({\mathbb{F}}_q)$, they are clustered around $1$ and $-1$ for odd $p$ and around $1$ for $p=2$.

References in corpus (1)

• Équirépartition de sommes exponentielles (travaux de Katz)