Abstract

This article provides a proof of the famous Prime Number Theorem by establishing an analogous statement of the same in terms of the second Chebyshev Function ψ(x). We shall be extensively using complex analytic techniques in addition to certain meromorphic properties of the Reimann Zeta Function ζ(s) and its Analytic Continuation Property a priori using Riemann’s Functional Equation in order to establish our desired result.

Keywords: Prime number theorem, Riemann zeta function, Holomorphic, Contour integral, Critical line