English

On the Non-vanishing of the D'Arcais Polynomials

Number Theory 2025-09-09 v1

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.

Keywords

Cite

@article{arxiv.2509.06123,
  title  = {On the Non-vanishing of the D'Arcais Polynomials},
  author = {Bernhard Heim and Markus Neuhauser},
  journal= {arXiv preprint arXiv:2509.06123},
  year   = {2025}
}