Zeros and roots of unity in character tables

2020/03/30 by Alexander R. Miller, Miller, Alexander R. · 1 citation
Engineering · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Surface Chemistry and Catalysis

paper · pdf · doi:10.48550/arxiv.2003.13238

openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any finite group G, Thompson proved that, for each χ∈ \rm 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∈ \rm Irr(G). We show that in many cases "more than a third" can be replaced by "more than half".

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• Denseness results for zeros and roots of unity in character tables

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