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Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function

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Abstract

Let Δ(x) and E(t) denote respectively the remainder terms in the Dirichlet divisor problem and the mean square formula for the Riemann zeta-function on the critical line. This article is a survey of recent developments on the research of these famous error terms in number theory. These include upper bounds, Ω-results, sign changes, moments and distribution, etc. A few open problems are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China

    Kai-Man Tsang

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  1. Kai-Man Tsang
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Correspondence to Kai-Man Tsang.

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Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday

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Tsang, KM. Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function. Sci. China Math. 53, 2561–2572 (2010). https://doi.org/10.1007/s11425-010-4068-6

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