Geodesic
On the Fourth Moment of the Riemann Zeta Functions
Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 101 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Atkinson proved in 1941 that $\int^\infty_0 e^{-t/T} |\zeta(1/2+it)|^4dt = TQ_4(\log T)+O(T^c)$ with $c = 8/9+\varepsilon$, where $Q_4(y)$ is a suitable polynomial in $y$ of degree four. We improve Atkinson's result by showing that $c=1/2$ is possible, and we provide explicit expressions for all the coefficients of $Q_4(y)$ and the closely related polynomial $P_4(y)$.
Classification : 11M06 
@article{PIM_1995_N_S_57_71_a10,
     author = {Aleksandar Ivi\'c},
     title = {On the {Fourth} {Moment} of the {Riemann} {Zeta} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {101 },
     year = {1995},
     volume = {_N_S_57},
     number = {71},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1995_N_S_57_71_a10/}
}
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Aleksandar Ivić. On the Fourth Moment of the Riemann Zeta Functions. Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 101 . http://geodesic.mathdoc.fr/item/PIM_1995_N_S_57_71_a10/