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arXiv · 2511.16276

On the Detection of Non-Roots of D'Arcais Polynomials

Bernhard Heim·Johann Stumpenhusen
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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.

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Bernhard Heim, Johann Stumpenhusen. 2025-11-20. On the Detection of Non-Roots of D'Arcais Polynomials. https://doi.org/10.1007/s40993-026-00705-6

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