Mathematical Sciences: Stark's Conjectures on Number Fields and Theory Fields

数学科学：斯塔克关于数域和理论域的猜想

• 批准号: 9302518
• 负责人: David Hayes
• 金额: $ 7.03万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302518&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stark; Conjectures; Number

This award supports the research of Professor Hayes to work in number theory. Professor Hayes will be addressing Stark's conjectures in class field theory. These conjectures are an ingenious and highly original answer to the questions raised by the famous 12 problem of Hilbert. Professor Hayes has given constructed proofs of the abelian Stark conjectures in function fields and he now hopes to apply his insights to the number field case. 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.

该奖项支持海耶斯教授的研究工作， 数论 海耶斯教授将在斯塔克的 类场理论的基本原理。 这些照片是一个 巧妙和高度原创性的答案所提出的问题， 著名的希尔伯特12问题 海耶斯教授给了 函数的交换斯塔克图的构造证明 他现在希望将他的见解应用于数字领域 案子 这是数论领域的研究。 数论 从整数和问题开始， 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已经成为开发新算法的重要工具， 计算机科学和新的电子纠错码。