# 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”.

## One Citation

### $p$-groups and zeros of characters

- 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?

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