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arXiv · 2509.06123

On the Non-vanishing of the D'Arcais Polynomials

Bernhard Heim·Markus Neuhauser
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Abstract

In this paper we invest in the non-vanishing of the Fourier coefficients of powers of the Dedekind eta function. This is reflected in non-vanishing properties of the D'Arcais polynomials. We generalize and improve results of Heim--Luca--Neuhauser and \.{Z}mija. We apply methods from algebraic number theory.

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Bernhard Heim, Markus Neuhauser. 2025-09-07. On the Non-vanishing of the D'Arcais Polynomials. https://arxiv.org/abs/2509.06123

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