Bounds for double zeta-functions
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TL;DRAbstract
In this paper we shall derive the order of magnitude for the double zeta-function of Euler-Zagier type in the region 0 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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In this paper we shall derive the order of magnitude for the double zeta-function of Euler-Zagier type in the region 0 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.
Keywords
Euler's formulaMathematicsExponential functionRiemann zeta functionType (biology)Pure mathematicsMathematics Subject ClassificationDouble exponential function
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