EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXVII, No. 28, pp. 17–29 (2003)

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On some mean value results involving $|\zeta({\textstyle{1\over2}} + it)|$

A. Ivic

Katedra za matematiku RGF-a, Univerzitet u Beogradu, Djusina 7, 11000 Beograd, Serbia and Montenegro, aivic@rgf.bg.ac.yu, aivic@matf.bg.ac.yu

Abstract: Several problems involving $E(T)$ and $E_2(T)$, the error terms in the mean square and mean fourth moment formula for $|\zt|$, are discussed. In particular it is proved that $$ \int_0^T E(t)E_2(T)t \ll T^{7/4}(\log T)^{7/2}\log\log T. $$

Keywords: Riemann zeta-function, mean square, mean fourth power, Hecke series

Classification (MSC2000): 11M06; 11F72, 11F66, 11M41

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Electronic fulltext finalized on: 17 Sep 2003. This page was last modified: 20 Jun 2011.

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