## 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:

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

**Prerequisites:** Basic working knowledge of number theory.

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

Professor Duke
| Math Courses | UCLA Department of Mathematics