EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXIX, No. 29, pp. 79–83 (2004)

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The circle and divisor problem

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: New proofs for the classical bounds $$ P(x) \ll x^{1/3}, \quad \Delta(x) \ll x^{1/3}\log x $$ are given. Here $P(x)$ denotes the error term in the classical circle, and $\Delta(x)$ in the classical divisor problem.

Keywords: circle problem; divisor problem; Voronoi summation formula; Selberg class

Classification (MSC2000): 11N37

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Electronic fulltext finalized on: 6 Oct 2003. This page was last modified: 20 Jun 2011.

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