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This is a Quantitative Study study.

October 3, 2025Open Access

On the Non-vanishing of the D'Arcais Polynomials

Key Points

The work reveals non-vanishing properties of d'Arcais polynomials in relation to Fourier series.
It generalizes and improves upon previous results by Heim, Luca, Neuhauser, and Żmija through novel approaches.
Algebraic number theory methods are applied to yield significant insights into these non-vanishing properties.
Understanding these relationships may enhance the theoretical framework of number theory and polynomial functions.

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 Żmija. We apply methods from algebraic number theory.

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Cite This Study

Heim et al. (Sun,) studied this question.

synapsesocial.com/papers/68e02f3cf0e39f13e7fa2631 https://doi.org/https://doi.org/10.48550/arxiv.2509.06123

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