On the Non-vanishing of the D'Arcais Polynomials
Bernhard Heim, Markus Neuhauser
Published: 2025/9/7
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.