Topics in Number Theory

数论专题

• 批准号: 9701101
• 负责人: Carl Pomerance
• 金额: $ 32.65万
• 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: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9701101&HistoricalAwards=false
• 关键词: Topics; Number; Theory

Pommerance 9701101 This award supports work on problems in analytic, computational, and additive number theory. One of the principal investigators will probe further the basic ideas behind some known algorithms, by making rigorous some of the established algorithms, and by developing the appropriate tools necessary to help analyze the next generation of algorithms. He will also study rigorous discrete logarithm algorithms for the multiplicative group of a finite field with bounded degree over its prime field, as well as several 'Erdos-type" problems in analytic number theory. The other principal investigator will try to obtain a more precise understanding of character sums by proving distribution results and lower bounds for the largest such sums. He also will study consequences of the abc-conjecture. Finally he will examine several of the infamous problems involving elliptic curves. 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.

Pommerance 9701101 该奖项支持分析，计算和加法数论问题的工作。 其中一位主要研究人员将进一步探索一些已知算法背后的基本思想，通过严格制定一些已建立的算法，并通过开发必要的适当工具来帮助分析下一代算法。 他还将研究严格的离散对数算法的乘法组的有限领域有界度超过其总理领域，以及几个“埃尔多斯型”问题的分析数论。 另一位主要研究者将通过证明分布结果和最大特征和的下限来更精确地理解特征和。 他还将研究abc猜想的结果。 最后，他将研究几个臭名昭著的问题，涉及椭圆曲线。 这是数论领域的研究。 数论从整数和一个整数被另一个整数整除等问题开始。 它是最古老的数学领域之一，最初是出于纯粹的美学原因而追求的。 然而，在过去的半个世纪，它已成为一个重要的工具，在开发新的算法，计算机科学和新的纠错码的电子。