This article is cited in 2 papers

A criterion for the convergence of the Mellin–Barnes integral for solutions to simultaneous algebraic equations

V. R. Kulikov

Siberian Federal University, Krasnoyarsk, Russia

Abstract: We obtain a criterion for the convergence of the Mellin–Barnes integral representing the solution to a general system of algebraic equations. This yields a criterion for a nonnegative matrix to have positive principal minors. The proof rests on the Nilsson–Passare–Tsikh Theorem about the convergence domain of the general Mellin–Barnes integral, as well as some theorem of a linear algebra on a subdivision of the real space into polyhedral cones.

Keywords: algebraic equations, Mellin–Barnes integral, hypergeometric functions, convergence domain.

UDC: 517.55

MSC: 35R30

Received: 25.06.2016

DOI: 10.17377/smzh.2017.58.312

 English version: Siberian Mathematical Journal, 2017, 58:3, 493–499

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