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

  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},
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

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The distribution of the number of summands in the partitions of a positive integer

It is easily seen that the number of partitions of n having k or less summands is equal to the number of partitions of n in which no summand exceeds k . Thus the preceding results can be applied to

Degrees, class sizes and divisors of character values

Abstract. In the character table of a finite group there is a tendency either for the character degree to divide the conjugacy class size or the character value to vanish. There is also a partial

Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements

We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions

Graduate Texts in Mathematics

Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully

Sur la distribution des cycles dans les permutations

  • C. R. (Doklady) Acad. Sci. URSS (N.S.)
  • 1942