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

Sameer Kulkarni; C. S. Rajan

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arXiv · 2110.02741

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

Sameer Kulkarni·C. S. Rajan

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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 $PGL_2(\mathbb F_q)$, they are clustered around $1$ and $-1$ for odd $p$ and around $1$ for $p=2$.

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Sameer Kulkarni, C. S. Rajan. 2021-10-06. On equidistribution of Gauss sums of cuspidal representations of $GL_d(\mathbb F_q)$. https://arxiv.org/abs/2110.02741

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