# 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} }

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

- Mathematics
- 2020

. 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…

### Groups with a small average number of zeros in the character table

- MathematicsJournal of Algebra
- 2022

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

- MathematicsRepresentation 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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