Mathematical Sciences: Topics in Analytic and Algorithmic Number Theory

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This grant supports the research of Professors C. Pomerance, Helmut Maier and Andrew Granville to work on problems in analytic, computational, and additive number theory. Professor Pomerance will continue to work on integer factoring algorithms, in particular the number field sieve. Professor Maier will work on the size of the coefficients of cyclotomic polynomials and irregularities in the distribution of primes. Professor Granville will also work on the distributions of the primes as well as sieve theory. 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.