This article is cited in 2 papers

Analytic continuation for solutions to the system of trinomial algebraic equations

Irina A. Antipova, Ekaterina A. Kleshkova, Vladimir R. Kulikov

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: In the paper, we deal with the problem of getting analytic continuations for the monomial function associated with a solution to the reduced trinomial algebraic system. In particular, we develop the idea of applying the Mellin–Barnes integral representation of the monomial function for solving the extension problem and demonstrate how to achieve the same result following the fact that the solution to the universal trinomial system is polyhomogeneous. As a main result, we construct Puiseux expansions (centred at the origin) representing analytic continuations of the monomial function.

Keywords: algebraic equation, analytic continuation, Puiseux series, discriminant locus, Mellin–Barnes integral.

UDC: 517.55+512.761

Received: 05.10.2019
Received in revised form: 09.11.2019
Accepted: 24.12.2019

Language: English

DOI: 10.17516/1997-1397-2020-13-1-114-130

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