Criteria for the integrality of $n$th roots of power series

John Pomerat; Armin Straub

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arXiv · 2406.12010

Criteria for the integrality of $n$th roots of power series

John Pomerat·Armin Straub

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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 Dieudonn\'e and Dwork that can be applied to this question as well.

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John Pomerat, Armin Straub. 2024-06-17. Criteria for the integrality of $n$th roots of power series. https://arxiv.org/abs/2406.12010

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