The analytic continuation and the order estimate of multiple Dirichlet series
Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 267-274.

Dans cet article, nous considérons que certaines séries de Dirichlet multiples, dont nous montrons le prolongement analytique en utilisant la formule intégrale de Mellin-Barnes. Des majorations de ces séries sont également obtenues.

Multiple Dirichlet series of several complex variables are considered. Using the Mellin-Barnes integral formula, we prove the analytic continuation and an upper bound estimate.

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     title = {The analytic continuation and the order estimate of multiple {Dirichlet} series},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
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Matsumoto, Kohji; Tanigawa, Yoshio. The analytic continuation and the order estimate of multiple Dirichlet series. Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 267-274. http://www.numdam.org/item/JTNB_2003__15_1_267_0/

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