PreprintCC BY-NC-ND 4.0arXiv
Zeros and Roots of Unity for Characters of Solvable Groups
Abstract
We prove Miller's conjectured bound for solvable groups: if G is a finite solvable group and χ∈Irr(G), then χ(g) is zero or a root of unity for at least half of the elements g∈ G. We also prove the same bound for monomial irreducible characters of arbitrary finite groups.
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BibTeX
@misc{bian2026zeros,
title = {{Zeros and Roots of Unity for Characters of Solvable Groups}},
author = {Fang Bian and Yong Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26842},
eprint = {2609.26842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26842},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Zeros and Roots of Unity for Characters of Solvable Groups
AU - Fang Bian
AU - Yong Yang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26842
UR - https://arxiv.org/abs/2609.26842
AB - We prove Miller's conjectured bound for solvable groups: if G is a finite solvable group and χ∈Irr(G), then χ(g) is zero or a root of unity for at least half of the elements g∈ G. We also prove the same bound for monomial irreducible characters of arbitrary finite groups.
ER -