Criteria for the integrality of 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 nth 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.
