Instructor: W. Banks

Description: This course focuses on modern methods in analytic number theory and will cover a variety of topics from the book by Iwaniec and Kowalski, including the elementary theory of prime numbers, characters, summation formulas, the theory of L-functions, sieve methods, estimates for exponential sums, zero-density estimates for the Riemann zeta function, the circle method. We will study other topics as time permits.

Text: H. Iwaniec and E. Kowalski, "Analytic Number Theory",
American Mathematical Society Colloquium Publications, 53.
American Mathematical Society, Providence, RI, 2004.

Prerequisites: Math 8220, or 8420, or 8425. Math 7900 together with instructor consent is also accepable.