Mathematical Sciences: Stark's Conjectures in Function Fields and Number Fields

该奖项支持马萨诸塞大学阿默斯特分校的David R. Hayes教授在数论和算术代数几何方面的研究。海斯博士的项目之一是对从实二次域定义的p进zeta函数的特殊值进行高精度的验证。另一个项目，更几何性质，是完全解决一个哥德巴赫问题在有限域上的函数场。与斯塔克猜想问题一样，海斯博士将在这些调查中广泛使用超级计算机。除了数数之外，数论是数学中最古老的分支，它研究的是整数的性质。在现代，数论中的问题为纯代数、分析和几何领域的新数学的创造提供了动力；数论的一些最新和最惊人的应用出现在理论计算机科学和编码理论中。

This award supports the research in number theory and arithmetic algebraic geometry of Professor David R. Hayes of the University of Massachusetts at Amherst. One of Dr. Hayes's projects is to carry out a high-precision verification of the Refined Stark Conjecture for special values of a p-adic zeta function defined from a real quadratic field. Another project, more geometric in nature, is to settle completely a Goldbach-like problem in function fields over finite fields. As with the Stark- Conjecture problem, Dr. Hayes will make extensive use of supercomputers in these investigations. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory.