Chapter 6 - THE PRIME NUMBER THEOREM

Abstract

This chapter discusses the prime number theorem. The subject of analytic number theory consists of the application of complex variable methods to the theory of numbers. The chapter discusses a connection between the Riemann zeta function and the properties of the prime numbers by means of the function L. The key property of the Riemann zeta function used in the proof of the prime number theorem is that ζ (z) ≠ 0 for Re z = 1. The Riemann zeta function is a special case of a Dirichlet series. The chapter also describes the connection between the Riemann zeta function and the gamma function.