Introduction to Analytic Number Theory Review of arithmetical functions, averages of arithmetical functions, elementary results on the distribution of prime numbers, Dirichlet characters, Dirichlet’s theorem on primes in arithmetic functions, Dirichlet series and Euler products, the Riemann zeta function and related objects, the prime number theorem. (Time permitting: advanced topics like sieves, bounds on exponential sums, zeros of functions. the circle method.)  Recommended books
- Apostol, T.M., Introduction to Analytic Number Theory, Springer-Verlag, 1976.
- Davenport, H., Multiplicative Number theory, 3rd edition, Springer, 2000
Prerequisites:
- MA 224 (complex Analysis) or equivalent
- An introductory course in Number Theory, or Consent of instructor