Submission date: 12 February 2024

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.

Mathematics Subject Classification: 14H05, 14P10, 14P15, 30B10, 32A05

Keywords and phrases:

Full text arXiv 2402.07524: pdf, ps.