Geodesic
Conditions for convergence of the Mellin--Barnes integral for solution to system of algebraic equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 339-346

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In the article we consider the Mellin–Barnes integral that corresponds to a monomial function of a solution to a system of $n$ algebraic equations in $n$ unknowns. We obtain the necessary condition for the convergence domain of the integral to be non empty. For $n=2$ we prove that this condition is also sufficient.
Keywords: Mellin–Barnes integral
Mots-clés : algebraic equations, convergence. 
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     author = {Vladimir R. Kulikov},
     title = {Conditions for convergence of the {Mellin--Barnes} integral for solution to system of algebraic equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {339--346},
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     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2014_7_3_a8/}
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Vladimir R. Kulikov. Conditions for convergence of the Mellin--Barnes integral for solution to system of algebraic equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 339-346. http://geodesic.mathdoc.fr/item/JSFU_2014_7_3_a8/