Mathematical Sciences: Number Theory with Emphasis on Algorithms and Algebraic Number Theory

数学科学：数论，重点是算法和代数数论

• 批准号: 9002939
• 负责人: Hendrik Lenstra
• 金额: $ 14.27万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1993-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002939&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Number; Theory; Emphasis

This award supports the research in number theory of Professor Hendrik Lenstra of the University of California at Berkeley. Dr. Lenstra has proposed to continue his research in several directions. In primality testing and factorization of large integers, he will study the newest factoring algorithm, known as the Number Field Sieve, and work on the practical implementation of a primality test. In algebraic number theory, he will investigate the existence of governing fields and study the class group structure of abelian fields. 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， 加州大学的亨德里克·伦斯特拉教授在 伯克利Lenstra博士提议继续他的研究， 几个方向。在素性测试和因式分解中， 大整数，他将学习最新的因式分解算法， 被称为号码场筛，并在实际工作 一个primality test。在代数数论中， 他将调查统治领域的存在， 阿贝尔域的类群结构 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。