Geodesic
Analytic continuations of a~general algebraic function by means of Puiseux series
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 9-19

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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. 
@article{TM_2012_279_a1,
     author = {I. A. Antipova and E. N. Mikhalkin},
     title = {Analytic continuations of a~general algebraic function by means of {Puiseux} series},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {9--19},
     publisher = {mathdoc},
     volume = {279},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_279_a1/}
}
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I. A. Antipova; E. N. Mikhalkin. Analytic continuations of a~general algebraic function by means of Puiseux series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 9-19. http://geodesic.mathdoc.fr/item/TM_2012_279_a1/