Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.18842

Authors: Charlton, Steven, Heim, Bernhard, Neuhauser, Markus, Stumpenhusen, Johann, Tröger, Robert

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7203942125

Cites: 18

Cited by:

Related to: 10