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ON THE ERROR TERM FOR THE FOURTH MOMENT OF THE RIEMANN ZETA-FUNCTION

Published online by Cambridge University Press:  01 August 1999

ALEKSANDAR IVIĆ
ALEKSANDAR IVIĆ
Affiliation:
Katedra Matematike RGF-a, Universiteta u Beogradu, Djušina 7, 11000 Beograd, Serbia (Yugoslavia); aleks@ivic.matf.bg.ac.yu
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Abstract

Let E2(T) denote the error term in the asymptotic formula for ∫T0[mid ]ζ(½+it)[mid ]4dt. It is proved that there exist constants A>0, B>1 such that for T[ges ]T0>0 every interval [T, BT] contains points T1, T2 for which

formula here

and that ∫T0[mid ]E2(t) [mid ]adt[Gt ]T1+(a/2) for any fixed a[ges ]1. These results complement earlier results of Motohashi and Ivić that ∫T0E2(t) dt[Lt ]T3/2 and that ∫T0E22(t) dt[Lt ]T2logCT for some C>0. Omega-results analogous to the above ones are obtained also for the error term in the asymptotic formula for the Laplace transform of [mid ]ζ(½+it)[mid ]4.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 21 - 32
Copyright
The London Mathematical Society 1999

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