Some factorization results for formal power series
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909047906631680 |
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| author | Garg, Rishu Singh, Jitender |
| author_facet | Garg, Rishu Singh, Jitender |
| contents | In this paper, we obtain some factorization results on formal power series over principle ideal domains with sharp bounds on number of irreducible factors. These factorization results correspondingly lead to irreducibility criteria for formal power series. The information about prime factorization of the constant term up to a unit and that of some higher order terms is utilized for the purpose. Further, using theory of Newton polygons for power series, we extend the classical Dumas irreducibility criterion to formal power series over discrete valuation domains, which in particular, yields several irreducibility criteria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some factorization results for formal power series Garg, Rishu Singh, Jitender Number Theory Commutative Algebra Algebraic Geometry 13F25, 11Y05, 13P05 In this paper, we obtain some factorization results on formal power series over principle ideal domains with sharp bounds on number of irreducible factors. These factorization results correspondingly lead to irreducibility criteria for formal power series. The information about prime factorization of the constant term up to a unit and that of some higher order terms is utilized for the purpose. Further, using theory of Newton polygons for power series, we extend the classical Dumas irreducibility criterion to formal power series over discrete valuation domains, which in particular, yields several irreducibility criteria. |
| title | Some factorization results for formal power series |
| topic | Number Theory Commutative Algebra Algebraic Geometry 13F25, 11Y05, 13P05 |
| url | https://arxiv.org/abs/2501.05375 |