题目: The Gauss circle problem and related topics

报告人：赵立璐（合肥工业大学）

时间: 2015年4月13日, 周一 下午15:00-16:30 

地点：管研楼1611

摘要： Let $/mathcal{N}(R)$ denote the number of integral points in the circle $$/{(x,y)/in /R^2: x^2+y^2/le R^2/}.$$ The classical result of Gauss asserts that $$/mathcal{N}(R)=/pi R^2+ E(R),$$ where the error term $E(R)$ satisfies $|E(R)|/le 2/sqrt{2}/pi R$. The Gauss circle problem is to investigate the asymptotic behavior of $E(R)$. We shall give a survey of developments on the research of the Gauss circle problem and related topics such as the Dirichlet divisor problem and the theory of Riemann zeta function.

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