Mathematical Sciences: Topics in Analytic and Algorithmic Number Theory

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This award supports the research in number theory of Professors Carl Pomerance and Helmut Maier of the University of Georgia. Dr. Pomerance's research will center on integer factoring algorithms and studies of the distribution in arithmetic progressions of integers with no large prime factor as well as properties of the sequence of divisors of an integer. Dr Maier's project is to continue his work on irregularities in the distribution of prime numbers in short intervals, and also to study the coefficients of the cyclotomic polynomials. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory.