Geodesic
On convergence of Mellin--Barnes integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 339-344

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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: Mellin–Barnes integral
Mots-clés : algebraic equations, convergence. 
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     author = {Artem V. Senashov},
     title = {On convergence of {Mellin--Barnes} integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {339--344},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a11/}
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Artem V. Senashov. On convergence of Mellin--Barnes integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 339-344. http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a11/