Geodesic
THE MEAN SQUARE OF THELOGARITHM OF THE ZETA-FUNCTION
Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 157-166

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Weinvestigate the function R(T,σ), which denotes the error term in theasymptotic formula for \int_0^T|\log\zeta(σ + it)|^2dt. It is shown thatR(T,σ) is uniformly bounded for σ \ge 1 and almostperiodic in the sense of Bohr for fixed σ \ge 1; hence R(T,σ)= Ω(1) when T \to \infty. In case {1 \over2}<σ<1 is fixed we can obtain the bound R(T,σ) \ll_εT\,^{(9-2σ)/8+ε}. 
BALAZARD, MICHEL; IVIĆ, ALEKSANDAR. THE MEAN SQUARE OF THELOGARITHM OF THE ZETA-FUNCTION. Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 157-166. doi: 10.1017/S0017089500020012
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     title = {THE {MEAN} {SQUARE} {OF} {THELOGARITHM} {OF} {THE} {ZETA-FUNCTION}},
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