Diophantine Methods for Exponential Sums, and Exponential Sums for Diophantine Problems

机译：指数求和的Diophantine方法以及Diophantine问题的指数和

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Recent developments in the theory and application of the Hardy-Littlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of exponential stuns are described first, concentrating on developments involving smooth Weyl sums. Next, arithmetic variants of classical inequalities of Bessel and Cauchy-Schwarz are discussed. Finally, some emerging connections between the circle method and arithmetic geometry are mentioned.

机译：讨论了Hardy-Littlewood方法的理论和应用方面的最新进展，重点是与对角色美菲汀问题相关的方面。首先介绍用于估计指数电晕平均值的最新有效微分方法，重点是涉及平滑Weyl和的发展。接下来，讨论Bessel和Cauchy-Schwarz经典不等式的算术变体。最后，提到了圆法和算术几何之间的一些新兴联系。

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来源
《International Congress of Mathematicians Vol.2: Invited Lectures Aug 20-28, 2002 Beijing》|2002年|p.207-217|共11页
会议地点 Beijing
作者
Trevor D. Wooley;
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作者单位

Department of Mathematics, University of Michigan, East Hall, 525 East, University Avenue, Ann Arbor, MI 48109-1109, USA;

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会议组织
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
the hardy-littlewood method; exponential sums; waring's problem; equations in many variables; rational points; representation problems;

机译：Hardy-Littlewood方法；指数和； Waring问题；许多变量的方程；理性点；表示问题;

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Diophantine Methods for Exponential Sums, and Exponential Sums for Diophantine Problems

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