MATHEMATICS COLLOQUIUM

     2PM MONDAY 17 MAY 2004 (TODAY) in 67-141


           Newman's short proof of the
              Prime Number Theorem

                Dr. Graham Norton
            Department of Mathematics,
             University of Queensland


Abstract

About two centuries ago, Legendre and Gauss gave conjectures on
the asymptotic behaviour of the number of primes less than or
equal to a positive real number x.  Nearly a century elapsed
before de la Vallee Poussin and Hadamard proved independently in
1896 that the number of primes less than or equal to x is
asymptotically x/log x. This is now known as the Prime Number
Theorem.

Standard modern proofs of the Prime Number Theorem date from the
1930's and use Wiener's Tauberian Theory for Fourier integrals.
In 1980, Newman gave a short proof of the Prime Number Theorem
based on an analytic Tauberian Theorem. We will give Newman's
breakthrough, which only uses a modicum of complex analysis.


All welcome.


-------------------
Pete Jenkins
pdj@maths.uq.edu.au