EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIV, No. 32, pp. 13–32 (2007)

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Subconvexity for the Riemann zeta-function and the divisor problem

M. N. Huxley and A. Ivic

School of Mathematics, University of Cardiff, 23 Senghenydd Road, Cardiff CF2 4AG, Great Britain
Katedra Matematike RGF-a, Universitet u Beogradu, Djusina 7, 11000 Beograd, Serbia

Abstract: A simple proof of the classical subconvexity bound $\zt \ll_\e t^{1/6+\e}$ for the Riemann zeta-function is given, and estimation by more refined techniques is discussed. The connections between the Dirichlet divisor problem and the mean square of $|\zt|$ are analysed.

Keywords: The Riemann zeta-function, subconvexity, the divisor problem, mean square of $|\zt|$, exponent pairs, Bombieri–Iwaniec method

Classification (MSC2000): 11M06, 11N37

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Electronic fulltext finalized on: 23 Sep 2007. This page was last modified: 20 Jun 2011.

© 2007 Mathematical Institute of the Serbian Academy of Science and Arts
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