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arXiv · 2609.26842

Zeros and Roots of Unity for Characters of Solvable Groups

Fang Bian·Yong Yang
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Abstract

We prove Miller's conjectured bound for solvable groups: if $G$ is a finite solvable group and $χ\in\Irr(G)$, then $χ(g)$ is zero or a root of unity for at least half of the elements $g\in G$. We also prove the same bound for monomial irreducible characters of arbitrary finite groups.

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Fang Bian, Yong Yang. 2026-09-22. Zeros and Roots of Unity for Characters of Solvable Groups. https://arxiv.org/abs/2609.26842

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