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Journal of Siberian Federal University. Mathematics & Physics, 2017, Volume 10, Issue 3, Pages 339–344
DOI: https://doi.org/10.17516/1997-1397-2017-10-3-339-344 (Mi jsfu563) 		 
On convergence of Mellin–Barnes integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables

Artem V. Senashov

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
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DOI: https://doi.org/10.17516/1997-1397-2017-10-3-339-344
Abstract: We consider the Mellin–Barnes integral that corresponds to a monomial function of a solution to a system of $n$ algebraic equations in $n$ variables. For $n=3$ we prove that a known necessary condition for convergence for the Mellin–Barnes integral is also sufficient.
Keywords: algebraic equations, Mellin–Barnes integral, convergence.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation NS-9149.2016.1
14.Y26.31.0006
This work was supported by a grant from the Russian government to conduct research under the direction of of leading scientists in the Siberian federal university of (contract no. 14.Y26.31.0006) and the Russian Federation President’s grant for support of leading scientific schools no. NS-9149.2016.1.
Received: 29.05.2016
Received in revised form: 10.11.2016
Accepted: 06.02.2017
Bibliographic databases:
Document Type: Article
UDC: 517.55+512.718
Language: English
Citation: Artem V. Senashov, “On convergence of Mellin–Barnes integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables”, J. Sib. Fed. Univ. Math. Phys., 10:3 (2017), 339–344
Citation in format AMSBIB
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\by Artem~V.~Senashov
\paper On convergence of Mellin--Barnes integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2017
\vol 10
\issue 3
\pages 339--344
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\crossref{https://doi.org/10.17516/1997-1397-2017-10-3-339-344}
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