Semialgebraicity of the convergence domain of an algebraic power series
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910348223709184 |
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| author | Kaiser, Tobias |
| author_facet | Kaiser, Tobias |
| contents | Given a power series in finitely many variables that is algebraic over the corresponding polynomial ring over a subfield of the reals, we show that its convergence domain is semialgebraic over the real closure of the subfield. This gives in particular that the convergence radius of a univariate Puiseux series that is algebraic in the above sense belongs to the real closure or is infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semialgebraicity of the convergence domain of an algebraic power series Kaiser, Tobias Complex Variables Algebraic Geometry 14H05, 14P10, 14P15, 30B10, 32A05 Given a power series in finitely many variables that is algebraic over the corresponding polynomial ring over a subfield of the reals, we show that its convergence domain is semialgebraic over the real closure of the subfield. This gives in particular that the convergence radius of a univariate Puiseux series that is algebraic in the above sense belongs to the real closure or is infinity. |
| title | Semialgebraicity of the convergence domain of an algebraic power series |
| topic | Complex Variables Algebraic Geometry 14H05, 14P10, 14P15, 30B10, 32A05 |
| url | https://arxiv.org/abs/2402.07524 |