Vol. 304, No. 1, 2020

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Bounds of double zeta-functions and their applications

Debika Banerjee, T. Makoto Minamide and Yoshio Tanigawa

Vol. 304 (2020), No. 1, 15–41
Abstract

In this paper, we shall improve the bounds on Euler–Zagier type double zeta-functions in the region 0 < Resj < 1 (j = 1,2) 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.

Keywords
Double zeta-function, Perron's formula, upper bound, mean square theorem
Mathematical Subject Classification 2010
Primary: 11M32
Secondary: 11M06
Milestones
Received: 26 March 2018
Revised: 8 July 2019
Accepted: 8 July 2019
Published: 18 January 2020
Authors
Debika Banerjee
Department of Mathematics
Indian Institute of Science Education and Research
Pune
India
Indraprastha Institute of Information Technology
Delhi
India
T. Makoto Minamide
Graduate School of Sciences and Technology for Innovation
Yamaguchi University
Yoshida
Yamaguchi
Japan
Yoshio Tanigawa
Graduate School of Mathematics
Nagoya University
Furo-cho, Nagoya
Japan
Nishisato
Meito, Nagoya
Japan