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.
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).
Received: 05.10.2019 Received in revised form: 09.11.2019 Accepted: 24.12.2019
Bibliographic databases:
Document Type:
Article
UDC:517.55+512.761
Language: English
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
\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}
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https://www.mathnet.ru/eng/jsfu824
https://www.mathnet.ru/eng/jsfu/v13/i1/p114
This publication is cited in the following 2 articles:
Irina A. Antipova, Ekaterina A. Kleshkova, “Parametrizations of limit positions for the discriminant locus of a trinomial system”, Zhurn. SFU. Ser. Matem. i fiz., 16:3 (2023), 318–329
Vladimir R. Kulikov, “Gipergeometricheskie ryady i integraly Mellina–Barnsa dlya nulei sistemy polinomov Lorana”, Zhurn. SFU. Ser. Matem. i fiz., 13:1 (2020), 87–96
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