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Bounds of double
zeta-functions and their applications
Debika Banerjee, T. Makoto Minamide and Yoshio Tanigawa |
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Vol. 304 (2020), No. 1, 15–41
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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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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 |
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| Yoshio Tanigawa | |
| Graduate School of Mathematics Nagoya University Furo-cho, Nagoya Japan |
Nishisato Meito, Nagoya Japan |
