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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 279, Pages 9–19
(Mi tm3436)
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This article is cited in 9 scientific papers (total in 9 papers)
Analytic continuations of a general algebraic function by means of Puiseux series
I. A. Antipova, E. N. Mikhalkin Siberian Federal University, Krasnoyarsk, Russia
Abstract:
A complete list of power series (centered at the point $x=0$) is obtained for the solution $y(x)$ of the general reduced algebraic equation $y^n+x_s y^{n_s}+\dots +x_1 y^{n_1}-1=0$. The domains of convergence of these series are described in terms of the amoeba of the discriminant of the equation. Sectorial domains through which one selected series is analytically continued to the other series are explicitly described.
Received in August 2012
Citation:
I. A. Antipova, E. N. Mikhalkin, “Analytic continuations of a general algebraic function by means of Puiseux series”, Analytic and geometric issues of complex analysis, Collected papers, Trudy Mat. Inst. Steklova, 279, MAIK Nauka/Interperiodica, Moscow, 2012, 9–19; Proc. Steklov Inst. Math., 279 (2012), 3–13
Linking options:
https://www.mathnet.ru/eng/tm3436 https://www.mathnet.ru/eng/tm/v279/p9
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Abstract page: | 543 | Full-text PDF : | 158 | References: | 105 |
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