On the mean square of the error term in the approximate functional equation for $ \zeta ^2(s) $

Abstract.

This paper deals with K(T), the error term in the asymptotic formula for the mean square of R(1/2 + it), the error term in the approximate functional equation for $\zeta ^2(s)$ when Re s = 1/2. The asymptotic formula for the integral of K(T) is obtained and the Laplace transform of |R(1/2 + it)|² is also evaluated.