On the Error Term for the Fourth Moment of the Riemann Zeta-Function |
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Authors: | Ivic Aleksandar |
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Institution: | Katedra Matematike RGF-a, Universiteta u Beogradu Djuina 7, 11000 Beograd, Serbia (Yugoslavia) aleks{at}ivic.matf.bg.ac.yu |
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Abstract: | Let E2(T) denote the error term in the asymptotic formula forT0|(+it)|4dt. It is proved that there exist constants A>0,B>1 such that for TT0>0 every interval T, BT] containspoints T1, T2 for which
and that T0|E2(t)|adt>>T1+(a/2) for any fixed a1. Theseresults complement earlier results of Motohashi and Ivi thatT0E2(t)dt<<T3/2 and that T0E22(t)dt<<T2logCT forsome C>0. Omega-results analogous to the above ones are obtainedalso for the error term in the asymptotic formula for the Laplacetransform of |(+it)|4. |
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