Math 285B
M W 1:45-3 PM MS 6221

Uniform distribution in analytic number theory
Professor: W. Duke

The distribution properties of arithmetic objects motivates a big part of analytic number theory. Perhaps the best known example is the study of primes and their distribution in arithmetic progressions. This course will concentrate on a different class of examples, starting with the distribution of quadratic residues and culminating in a proof that CM points are uniformly distributed. A recent application of this to the traces of singular moduli will be given.

Topics:

1. Uniform distribution mod 1 and Weyl's criterion
2. Theorem of Burgess
3. Subconvexity of L-functions
4. Siegel's estimate
5. Distribution of CM points

Prerequisites: Basic working knowledge of number theory.

Texts: Various references will be used, including Iwaniec and Kowalski: Analytic Number Theory.