On the Detection of Non-Roots of D'Arcais Polynomials
Number Theory
2025-11-21 v1
Abstract
The Lehmer conjecture states that the non-constant Fourier coefficients of the 24th power of the Dedekind eta function are non-zero. In a recent preprint, Neuhauser and the first author exploited an easily accessible tool from algebraic number theory, namely the Dedekind--Kummer Theorem, to prove the non-vanishing of the Fourier coefficients of certain powers of the Dedekind eta function at roots of unity. We extend the application of this method to enlarge the scope of non-roots of the related D'Arcais polynomials.
Keywords
Cite
@article{arxiv.2511.16276,
title = {On the Detection of Non-Roots of D'Arcais Polynomials},
author = {Bernhard Heim and Johann Stumpenhusen},
journal= {arXiv preprint arXiv:2511.16276},
year = {2025}
}