• Corpus ID: 251718679

Zeros and roots of unity in character tables

@inproceedings{Miller2020ZerosAR,
title={Zeros and roots of unity in character tables},
author={Alexander R. Miller},
year={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 average class g G , χ ( g ) is a root of unity or zero for more than a third of the irreducible characters χ ∈ Irr( G ). We show that in many cases “more than a third” can be replaced by “more than half”.
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Tables from this paper

• Mathematics
• 2023
. Fix a prime p and an integer n ≥ 0. Among the non-linear irreducible characters of the p -groups of order p n , what is the minimum number of elements that take the value 0?

References

SHOWING 1-10 OF 17 REFERENCES

• 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.
• Mathematics
International Mathematics Research Notices
• 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 $n\to \infty$.
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