Mathematical Sciences: Effective Measures of Irrationality for Algebraic Numbers

9622556 Vaaler这笔赠款支持J.Vaaler教授关于代数数逼近的有效度量问题的研究。他希望将最近在立方体田块中发现的有效措施的技术推广到更高程度的田块。他希望通过寻找戴森引理的一种改进的多元形式来做到这一点。这是数论领域的研究。数论始于整数和诸如一个整数被另一个整数整除的问题。它是最古老的数学领域之一，最初是出于纯粹的美学原因。然而，在过去的半个世纪里，它已经成为开发计算机科学的新算法和电子产品的新纠错码的必要工具。?？

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. ??