Syllabus
The course will consist of a selection of the following topics. Prime number theorem.
Dirichlet's theorem on primes in arithmetic progressions. Irrationality of zeta(3).
Introduction to modular forms. Shnirelman's theorem on primes and Selberg's sieve.
Vinogradov's three primes theorem. Freiman's theorem in additive number theory.
T. Tao's proof of Szemeredi's theorem on arithmetic progressions, ...
Annotation
The course will cover some classic as well as some recent results of analytic and combinatorial number theory.