Work

On the detection of non-roots of D’Arcais polynomials

Year: 2026

Type: article

Abstract: The Lehmer conjecture states that the non-constant Fourier coefficients of the 24th power of the Dedekind eta function are non-zero. Recently, Neuhauser and the first author exploited an easily accessible tool from algebraic number theory, namely the Dedekind–Kummer Theorem, to prove the non-vanishing of the Fourier coefficients of certain powers of the Dedekind eta function at roots of unity. We extend the application of this method to enlarge the scope of non-roots of the related D’Arcais polynomials.

Source: Research in Number Theory

DOI: 10.1007/s40993-026-00705-6

Authors: Bernhard Heim, Johann Stumpenhusen

Institution: University of Cologne

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funder: Universität zu Köln