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 with respect to the Haar measure. However, for representations of `$PGL_2(\mathbb{F}_q)$`

, they are clustered around `$1$`

and `$-1$`

for odd `$p$`

and around `$1$`

for `$p=2$`

. This is joint work with Sameer Kulkarni.

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Last updated: 08 Dec 2023