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.
In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.
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