Mathematical Sciences: Effective Measures of Irrationality for Algebraic Numbers

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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. ??