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J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 1, Pages 114–130 (Mi jsfu824)  

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.

Funding Agency Grant Number
Foundation for the Development of Theoretical Physics and Mathematics BASIS 18-1-7-60-1
18-1-7-60-2
Ministry of Education and Science of the Russian Federation 1.2604.2017/PCh
The first author was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS" (no. 18-1-7-60-1). The second author was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS" (no. 18-1-7-60-2). The third author was supported by the grant of the Ministry of Education and Science of the Russian Federation (no. 1.2604.2017/PCh).


DOI: https://doi.org/10.17516/1997-1397-2020-13-1-114-130

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UDC: 517.55+512.761
Received: 05.10.2019
Received in revised form: 09.11.2019
Accepted: 24.12.2019
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Citation: Irina A. Antipova, Ekaterina A. Kleshkova, Vladimir R. Kulikov, “Analytic continuation for solutions to the system of trinomial algebraic equations”, J. Sib. Fed. Univ. Math. Phys., 13:1 (2020), 114–130

Citation in format AMSBIB
\Bibitem{AntKleKul20}
\by Irina~A.~Antipova, Ekaterina~A.~Kleshkova, Vladimir~R.~Kulikov
\paper Analytic continuation for solutions to the system of trinomial algebraic equations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 1
\pages 114--130
\mathnet{http://mi.mathnet.ru/jsfu824}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-1-114-130}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000514843200011}


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