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

数学科学：函数域和数域中的斯塔克猜想

• 批准号: 8903512
• 负责人: David Hayes
• 金额: $ 5.66万
• 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: 1989
• 资助国家: 美国
• 起止时间: 1989-11-01 至 1992-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903512&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stark; Conjectures; Function

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.

该奖项支持数论研究， 算术代数几何学的教授大卫R。海耶斯 马萨诸塞州阿默斯特大学。海耶斯医生的 项目是进行高精度的验证， p-adic zeta特殊值的精化Stark猜想 由真实的二次域定义的函数。另一个项目， 更几何的性质，是完全解决一个哥德巴赫式 有限域上的函数域问题和史塔克一样 猜想问题，海耶斯博士将广泛使用 超级计算机在这些调查中。 除了计数，数论，这是研究 整数的性质，是最古老的分支， 数学在现代，数论中的问题 为新数学的产生提供了动力， 纯代数，分析和几何领域;一些最重要的 数论最近最令人惊讶的应用是 出现在理论计算机科学和编码理论中。