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On the mean square formula of the error term in the Dirichlet divisor problem

Published online by Cambridge University Press:  01 March 2009

YUK-KAM LAU  and
KAI-MAN TSANG
YUK-KAM LAU
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong. e-mail: yklau@maths.hku.hk, kmtsang@maths.hku.hk
KAI-MAN TSANG
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong. e-mail: yklau@maths.hku.hk, kmtsang@maths.hku.hk
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Abstract

Let F(x) be the remainder term in the mean square formula of the error term Δ(t) in the Dirichlet divisor problem. We improve on the upper estimate of F(x) obtained by Preissmann around twenty years ago. The method is robust, which applies to the same problem for the error terms in the circle problem and the mean square formula of the Riemann zeta-function.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 277 - 287
Copyright
Copyright © Cambridge Philosophical Society 2008

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