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: 9206784
• 负责人: Carl Pomerance
• 金额: $ 45.91万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9206784&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Analytic; Algorithmic

This grant supports the research of Professors C. Pomerance, Helmut Maier and Andrew Granville to work on problems in analytic, computational, and additive number theory. Professor Pomerance will continue to work on integer factoring algorithms, in particular the number field sieve. Professor Maier will work on the size of the coefficients of cyclotomic polynomials and irregularities in the distribution of primes. Professor Granville will also work on the distributions of the primes as well as sieve theory. 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.

该基金支持C教授的研究。波默兰斯， 赫尔穆特·梅尔和安德鲁·格兰维尔将致力于分析， 计算和加法数论。 波默兰斯教授 将继续致力于整数分解算法， 特别是数域筛选。 迈尔教授将致力于 分圆多项式系数的大小， 素数分布的不规则性格兰维尔教授 也将致力于素数的分布以及筛选 理论 这是数论领域的研究。 Number 理论开始于整数和问题，如 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。