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arXiv · 2402.07524

Semialgebraicity of the convergence domain of an algebraic power series

Tobias Kaiser
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Abstract

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.

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Tobias Kaiser. 2024-02-12. Semialgebraicity of the convergence domain of an algebraic power series. https://arxiv.org/abs/2402.07524

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