Mathematical Sciences: Studies in Analytic Number Theory

数学科学：解析数论研究

• 批准号: 9107605
• 负责人: Hugh Montgomery
• 金额: $ 28.66万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1995-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107605&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Analytic; Number

This grant supports the research of Professor H. Montgomery as principal investigator, Professor David Masser as a research associate and Dr. Jeffrey Thunder as a post-doctoral associate. Professor Montgomery will work on problems in analytic and additive number theory. In particular, he will concentrate on sieve methods and the geometric properties of the zeta function. Professor Masser will work on Diophantine approximation particularly as it relates to arithmetic geometry. He will also study large period matrices and endomorphism rings of Abelian varieties. Dr. Thunder will try to give explicit asymptotic estimates for the number of points of bounded height on certain varieties. He also intends to study the Thue equation. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.

这笔赠款支持H.蒙哥马利教授作为首席研究员、大卫·马瑟教授作为研究助理和杰弗里·雷德博士作为博士后助理进行的研究。蒙哥马利教授将研究解析和加法数论中的问题。特别是，他将专注于筛法和Zeta函数的几何性质。马瑟教授将研究丢番图逼近，特别是与算术几何有关的问题。他还将研究大周期矩阵和Abel簇的自同态环。雷德博士将尝试对某些变种上有界高度的点数给出显式的渐近估计。他还打算研究图厄方程。这是数论领域的研究。数论始于整数和诸如一个整数被另一个整数整除的问题。它是最古老的数学领域之一，最初是出于纯粹的美学原因。然而，在过去的半个世纪里，它已经成为开发计算机科学的新算法和电子产品的新纠错码的必要工具。