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Abstract
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In this paper, we shall improve the bounds on Euler–Zagier type double zeta-functions in
the region
which
provides a positive answer to a conjecture posed by Kiuchi and Tanigawa (2006). As
an application, we improve the error term that appears in the asymptotic formula for
the moment of the double zeta-function.
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Keywords
Double zeta-function, Perron's formula, upper bound, mean
square theorem
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Mathematical Subject Classification 2010
Primary: 11M32
Secondary: 11M06
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Milestones
Received: 26 March 2018
Revised: 8 July 2019
Accepted: 8 July 2019
Published: 18 January 2020
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