Mathematical Sciences: Studies in Analytic Number Theory

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This grant supports the research of Professor H. Montgomery as principal investigator, Professor David Masser as a research associate and Dr. Jeffrey Thunder as a post-doctoral associate. Professor Montgomery will work on problems in analytic and additive number theory. In particular, he will concentrate on sieve methods and the geometric properties of the zeta function. Professor Masser will work on Diophantine approximation particularly as it relates to arithmetic geometry. He will also study large period matrices and endomorphism rings of Abelian varieties. Dr. Thunder will try to give explicit asymptotic estimates for the number of points of bounded height on certain varieties. He also intends to study the Thue equation. 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.