### Course Description :

This course will provide an introduction to analytic number theory, the branch of modern number theory that uses real and complex analysis to study the distribution of arithmetic objects, especially the prime numbers. Covered topics include: mean values of arithmetic functions, the prime number estimates of Chebyshev and of Mertens, Dirichlet series and Euler products, the theory of the Riemann zeta function, Dirichlet characters and Dirichlet $L$-functions, the proof of the prime number theorem, the distribution of prime numbers in arithmetic progressions.