MA 352: Introduction to Analytic Number Theory
Credits: 3:0
Pre-requisites :
- Introductory courses in basic number theory
- Complex analysis
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, Riemann zeta function and related objects, The prime number theorem.
(Time permitting: More advanced topics like Sieves, bounds on exponential sums, zeros of zeta functions, circle method etc.)
Suggested books and references:
- H. Davenport., Multiplicative Number Theory, Springer GTM 74 (third ed.) 2000.
- Tom. M. Apostol., Introduction to Analytic Number Theory, Springer-Verlag, 1976.