Equidistribution of high traces of random matrices over finite fields and cancellation in character sums of high conductor

Ofir Gorodetsky, Valeriya Kovaleva

Let $g$ be a random matrix distributed according to uniform probability measure on the finite general linear group ${\mathrm{GL}}_n({\mathbb{F}}_q)$. We show that $\mathrm{Tr}(g^k)$ eq…