Bounds of double zeta-functions and their applications

Abstract

In this paper, we shall improve the bounds on Euler-Zagier type double zeta-functions in the region 0 < Re sj < 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.