#### 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 $\left(j=1,2\right)$ 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
Primary: 11M32
Secondary: 11M06