PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 57(71) (dedicated to Djuro Kurepa), pp. 101110 (1995) 

On the fourth moment of the Riemann zeta functionsAleksandar Ivi\'cKatedra za matematiku, RudarskoGeoloski fakultet, Beograd, YugoslaviaAbstract: 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 (MSC2000): 11M06 Full text of the article:
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