# Many Zeros of Many Characters of GL(n,q)

@article{Gallagher2020ManyZO,
title={Many Zeros of Many Characters of GL(n,q)},
author={Patrick X. Gallagher and Michael Larsen and Alexander R. Miller},
journal={International Mathematics Research Notices},
year={2020}
}
• Published 3 September 2019
• Mathematics
• International Mathematics Research Notices
For $G=\textrm{GL}(n,q)$, the proportion $P_{n,q}$ of pairs $(\chi ,g)$ in $\textrm{Irr}(G)\times G$ with $\chi (g)\neq 0$ satisfies $P_{n,q}\to 0$ as $n\to \infty$.
3 Citations

### Zeros and roots of unity in character tables

. For any ﬁnite group G , Thompson proved that, for each χ ∈ Irr( G ), χ ( g ) is a root of unity or zero for more than a third of the elements g ∈ G , and Gallagher proved that, for each larger than

### The sparsity of character tables of high rank groups of Lie type

• Mathematics
Representation Theory of the American Mathematical Society
• 2020
In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.

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