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

作　　者：TSANG Kai-Man 

机构地区：[1]Department of Mathematics,The University of Hong Kong

出　　处：《Science China Mathematics》2010年第9期2561-2572,共12页中国科学：数学（英文版）

摘　　要：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.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.

关 键 词：DIVISOR PROBLEMS Riemann’s ZETA-FUNCTION mean VALUES 

分 类 号：O156[理学—数学]