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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月10日

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  • Bernhard Heim,
  • Johann Stumpenhusen

摘要

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.