Sindre Becker: Primtalssatsen genom Newmans Tauberiska sats för Laplace-transformationen och Riemanns zetafunktion

Abstract

This work will prove the prime number theorem with Newman's version of the proof. The work will start with Riemann's zeta function and how it behaves in the complex halfplane with positive real part, to then start with the Laplace transform and Newman's Tauberian theorem about the transform. Lastly this will be combined into proving the prime number theorem.