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Bounds for double zeta-functions

Isao KiuchiYoshio Tanigawa — 2006

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region 0 s j < 1 ( j = 1 , 2 ) .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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