On the mean value formula for the non-symmetric form of the approximate functional equation of \(\zeta^2(s)\) in the critical strip (Q2714216)

The author considers the error term in the approximate functional equation for \(\zeta ^2(s)\) with \(s=\sigma +it\), \(0\leq \sigma \leq 1\), \(t\geq 1\), in the case when the two sums occurring in this formula are of the length \(r^{\pm 1}t/2\pi \) for a rational number \(r\). Previously he had obtained an asymptotic formula for the mean square of the error term in the case \(\sigma =1/2\) [Tokyo J. Math. 17, 191-200 (1994; Zbl 0805.11059)], and this is now generalized to all \(\sigma \in [0,1]\). To this end, the general case is first reduced to \(\sigma =1/2\) by a suitable approximation, and the earlier result is then invoked.