Lecture 1:-
Unique Factorization Theorem Infinitude of primes Statement of PNT Cramer model Failure of Cramer model
Lecture 2:-
Open questions on primes Recent achievements of prime number theory The Riemann Zeta-function Euler product Analytic continuation and functional equation (via theta function)
Lecture 3:-
Analytic continuation and functional equation (continued) Hadamard product and its logarithmic derivative N(T) and S(T)
Lecture 4:-
N(T) and S(T) (continued) Non-vanishing on the 1-line Proof of PNT
Lecture 5:-
Proof of PNT (continued) Weil type Explicit formulae
Lecture 6:-
Characters Dirichlet L-functions
Pre-requisites:-
Undergrad complex analysis Prpoerties of the gamma function Undergrad algebra (Z is a UFD)
Recommended text:-
Davenport, Multiplicative Number Theory
