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arXiv · 2408.14046

The Divisibility of $\mathrm{GL}(n, q)$ Character Values

Varun Shah·Steven Spallone
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Abstract

Let $q$ be a prime power, and $d$ a positive integer. We study the proportion of irreducible characters of $\mathrm{GL}(n,q)$ whose values evaluated on a fixed matrix $g$ are divisible by $d$. As $n$ approaches infinity, this proportion tends to $1$ when $q$ is coprime to $d$. When $q$ and $d$ are not coprime, and $g=1$, this proportion is bounded above by $\frac{1}{q}$.

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Varun Shah, Steven Spallone. 2024-08-26. The Divisibility of $\mathrm{GL}(n, q)$ Character Values. https://arxiv.org/abs/2408.14046

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