Let Δ(x) denote the error term in the Dirichlet divisor problem, and
E(T) the error term in the asymptotic formula for the mean square of
∣ζ(1/2+it)∣. If E∗(t)=E(t)−2πΔ∗(t/2π) with Δ∗(x)=−Δ(x)+2Δ(2x)−21Δ(4x), then we obtain the
asymptotic formula ∫0T(E∗(t))2dt=T4/3P3(logT)+Oϵ(T7/6+ϵ), where P3 is a polynomial of degree three in
logT with positive leading coefficient. The exponent 7/6 in the error term
is the limit of the method.Comment: 10 page