Analytic continuations of a general algebraic function by means of Puiseux series

DOI10.1134/S0081543812080020zbMath1298.32001OpenAlexW1984071605MaRDI QIDQ461029

Evgeny Mikhalkin, Irina A. Antipova

Publication date: 9 October 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543812080020

zbMATH Keywords

power seriesanalytic continuationalgebraic equation

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Power series, series of functions of several complex variables (32A05)

Related Items (8)

Unnamed Item ⋮ The monodromy of a general algebraic function ⋮ An explanation of Mellin's 1921 paper ⋮ Convergence of two-dimensional hypergeometric series for algebraic functions ⋮ On solutions and Waring’s formulas for systems of $n$ algebraic equations for $n$ unknowns ⋮ Coamoebas of Discriminants of Tetranomials ⋮ Domains of Convergence for A-hypergeometric Series and Integrals ⋮ Analytic Continuation for Solutions to the System of Trinomial Algebraic Equations

Cites Work

• Monodromy of \(A\)-hypergeometric functions
• Algebraicity of the Appell-Lauricella and Horn hypergeometric functions
• Solving algebraic equations in terms of \(\mathcal A\)-hypergeometric series
• Studying the multiple Mellin--Barnes integrals by means of multidimensional residues
• Hypergeometric solutions of some algebraic equations
• Inversion of many-dimensional Mellin transforms and solutions of algebraic equations
• On Hilbert's thirteenth problem and related questions
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