Mathematical Sciences: Topics in Analytic and Algorithmic Number Theory

数学科学：解析和算法数论主题

• 批准号: 9002538
• 负责人: Carl Pomerance
• 金额: $ 16.85万
• 依托单位: University of Georgia Research Foundation Inc
• 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: 1990-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002538&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Analytic; Algorithmic

This award supports the research in number theory of Professors Carl Pomerance and Helmut Maier of the University of Georgia. Dr. Pomerance's research will center on integer factoring algorithms and studies of the distribution in arithmetic progressions of integers with no large prime factor as well as properties of the sequence of divisors of an integer. Dr Maier's project is to continue his work on irregularities in the distribution of prime numbers in short intervals, and also to study the coefficients of the cyclotomic polynomials. 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， 密歇根大学的卡尔·波默兰斯和赫尔穆特·梅尔教授 格鲁吉亚。波默兰斯博士的研究将集中在整数 因子分解算法和分布的研究 没有大素因子的整数的算术级数， 以及整数的约数序列的性质。博士 迈尔的项目是继续他的工作， 素数在短区间内的分布，以及 研究分圆多项式的系数。 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。