MATH-UA.394.001, Spring, 2017
Tuesday & Thursday, 12:20 - 1:45
Room 312, Warren Weaver Hall
An introduction to analytic methods in number theory. Some goals are Dirichlet’s theorem on prime numbers in an arithmetic progression, the proof of Prime Number Theorem using the Riemann zeta function, Van der Corput’s theorem about lattice points in a circle, and some work of Hardy and Ramanujan on partitions. Mathematical technique is developed as needed. This includes basics of complex function theory and integration, Fourier analysis, and finite abelian groups (for Dirichlet’s theorem).
This class will be taught in an undergraduate style. It will cover a few selected topics rather than giving a thorough foundation of modern analytic number theory as one would expect from a graduate class.
Students must have Analysis I or specific permission of the instructor. Each of these is helpful but not required: Algebra I, Theory of Numbers, Complex Variables