Criteria for the integrality of $n$th roots of power series
Volume 215 / 2024
Acta Arithmetica 215 (2024), 1-10
MSC: Primary 11B75; Secondary 13F25
DOI: 10.4064/aa230425-4-4
Published online: 19 June 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 them with a general integrality criterion due to Dieudonné and Dwork that can be applied to this question as well.
