This is an elementary course in analytic number theory whose aim is to give an introductory account of some basic results and techniques in this area. The beginning of this theory can be traced back to Dirichlet’s memoir of 1837, in which he proved the existence of prime numbers in arithmetic progressions. The course divides naturally in two parts. In the first part, after a brief review of complex analysis, we will prove the celebrated Prime Number Theorem and Dirichlet’s theorem on the distribution of primes in arithmetic progressions. The proofs exploit analytic properties of the zeta function and Dirichlet L-functions.
The second part of the course is a brief introduction into the theory of Modular forms. We will closely follow Serre's "a course in arithmetic''.
Grading: The grade in this course is based on one presentation in the last two weeks of the semester. You can pick any relevant topic after consultation with me. You can find a list of suggestions here.