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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12010 |
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| _version_ | 1866916290455666688 |
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| author | Pomerat, John Straub, Armin |
| author_facet | Pomerat, John Straub, Armin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Criteria for the integrality of $n$th roots of power series Pomerat, John Straub, Armin Number Theory 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. |
| title | Criteria for the integrality of $n$th roots of power series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.12010 |