Chennai Mathematical Institute


3.30 pm, Seminar Hall
The Prime number Theorem

M.S. Raghunathan
NCM, IIT Bombay.


The Prime Number Theorem is arguably the most celebrated theorem in Number Theory. The theorem was proved in 1896 by Jacques Hadamard and Charles de la Vallee Poussin. In 1948 Atle Selberg and Paul Erdos (independently) gave the same proof of the theorem without the use of complex analysis (dubbed "elementary" because of that). The Hadamard - de la vallee Poussin proof has two steps: (i)the non-vanishing of the Zeta function on $Re s = 1$ and (ii) deduction of the asymptotic behaviour of $\pi(x)$ (= number of primes less than or equal to $x$). The second step was simplified a great deal by D J Newman in 1980. In this talk we will give the proof of the theorem along the lines of Newman.