Bounds for double zeta-functions. (English) Zbl 1170.11317
Summary: In this paper we shall derive the order of magnitude for the double zeta-function of Euler-Zagier type in the region \(0\leq\operatorname{Re} s_j<1\) \((j=1,2)\). First we prepare the Euler-Maclaurin summation formula in a suitable form for our purpose, and then we apply the theory of double exponential sums of van der Corput’s type.
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