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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