The analytic theory of L-functions
The course will cover the theory of L-functions, from an analytic number theory perspective. Topics to be covered include:
Definitions and basic properties of L-functions (Euler product, functional equation, analytic continuation)
Arithmetical applications
Methods of computation, such as the approximate functional equation
Methods of estimation, i.e., the subconvexity problem
Mean value properties, and connections to random matrix theory
Distribution of zeros and nonvanishing results
The textbook to be used is Iwaniec-Kowalski, Analytic Number Theory.