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Criteria for the integrality of nth roots of power series

Criteria for the integrality of nth roots of power series
John Pomerat, Armin Straub — Acta Arithmetica — to appear — 2024

Abstract

Heninger, Rains and Sloane raised the question of which power series with integer coefficients can be written as the \(n\)th power of another power series with integer coefficients and constant term \(1\). We provide necessary and sufficient conditions, as well as compare with a general integrality criterion due to Dieudonné and Dwork that can be applied to this question as well.

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BibTeX

@article{integrality-powerseries-2024,
    author = {John Pomerat and Armin Straub},
    title = {Criteria for the integrality of nth roots of power series},
    journal = {Acta Arithmetica},
    year = {2024},
    doi = {10.4064/aa230425-4-4},
}