Mathematical Sciences: Problems in Analytic Number Theory

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Montgomery This award funds the research in analytic number theory of Professor Hugh Montgomery. Prof. Montgomery will study a number of outstanding problems in multiplicative and additive number theory including the Riemann Hypothesis. In one part of the project he hopes to construct a general technique for determining optimal sieve methods. Such a technique would have wide application. The field of analytic number theory applies the techniques of calculus to the discrete realm of the whole numbers. Calculus was developed to aid the analysis of continuous mathematical objects. The idea of using continuous methods to investigate discrete objects is two centuries old, but with the work of the modern analytic number theorists such as Professor Montgomery, the field has had a new rebirth. ***