Mathematical Sciences: Studies in Analytic Number Theory

该基金支持H. Montgomery教授担任首席研究员，David Masser教授担任副研究员，Jeffrey Thunder博士担任博士后研究员。蒙哥马利教授将研究解析数论和加性数论的问题。特别是，他将专注于筛法和zeta函数的几何性质。Masser教授将研究丢番图近似，特别是与算术几何相关的近似。他还将研究大周期矩阵和阿贝尔变体的自同态环。桑德博士将尝试给出某些品种上有界高度点的数目的显式渐近估计。他还打算研究Thue方程。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。

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.