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PreprintCC BY 4.0arXiv

A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz

  • Steven Charlton
  • Bernhard Heim
  • Markus Neuhauser
  • Johann Stumpenhusen
  • Robert Tröger
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Abstract

Heretofore, the second and third author conjectured that the D'Arcais polynomials, related to the coefficients of the powers of the Dedekind η-function, are Hurwitz polynomials except for a root at the origin. We show that this does in fact not hold for a positive proportion of all natural numbers.

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Cite

BibTeXRIS
BibTeX
@misc{charlton2026positive,
  title = {{A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz}},
  author = {Steven Charlton and Bernhard Heim and Markus Neuhauser and Johann Stumpenhusen and Robert Tröger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.18842},
  eprint = {2608.18842},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.18842},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz
AU  - Steven Charlton
AU  - Bernhard Heim
AU  - Markus Neuhauser
AU  - Johann Stumpenhusen
AU  - Robert Tröger
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2608.18842
UR  - https://arxiv.org/abs/2608.18842
AB  - Heretofore, the second and third author conjectured that the D'Arcais polynomials, related to the coefficients of the powers of the Dedekind η-function, are Hurwitz polynomials except for a root at the origin. We show that this does in fact not hold for a positive proportion of all natural numbers.
ER  -