Mean Square of Double Zeta-function

Abstract

Lately, Kiuchi and Minamide studied the mean square of the double zeta-function $\zeta_2(\sigma_{1}+it_1, \sigma_{2}+it_2)$ with respect to $ t_1 $ in the critical region. In this paper, using a new upper bound of $\zeta_{2}(\sigma_{1}+it_1, \sigma_{2}+it_2)$ we improve the results on the mean square of $\zeta_{2}(\sigma_{1}+it_{1}, \sigma_{2}+it_{2})$, obtained by Kiuchi and Minamide.