Mathematical Sciences: Effective Measures of Irrationality for Algebraic Numbers

9622556瓦勒本基金资助瓦勒教授研究代数数近似值的有效测度问题。他希望将最近发现的在立方领域采取有效措施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一种改进的多元形式来实现这一目标。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。? ?

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. ??