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.