Mathematical Sciences: Effective Measures of Irrationality for Algebraic Numbers

数学科学：代数数无理性的有效度量

• 批准号: 9622556
• 负责人: Jeffrey Vaaler
• 金额: $ 7.5万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-15 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622556&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Effective; Measures; Irrationality

9622556 Vaaler This grant supports the research of Professors J. Vaaler to work on problems in effective measures for approximations of algebraic numbers. He hopes to extend techniques recently discovered for effective measures in cubic fields to fields of higher degree. He hopes to do this by searching for an improved multivariate form of Dyson's lemma. 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. ??

小行星9622556 该补助金支持教授J. Vaaler的研究，以解决代数数近似的有效措施问题。他希望将最近发现的在立方领域有效测量的技术推广到更高程度的领域。他希望通过寻找戴森引理的改进的多元形式来做到这一点。 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。 ??