Title

A Derivation of π(n) Based on a Stability Analysis of the Riemann-Zeta Function

Document Type

Article

Publication Date

4-2010

Department

Department of Physics and Computer Science

Abstract

The prime-number counting function π(n), which is significant in the prime number theorem, is derived by analyzing the region of convergence of the real-part of the Riemann- Zeta function using the unilateral z-transform. In order to satisfy the stability criteria of the z-transform, it is found that the real part of the Riemann-Zeta function must converge to the prime-counting function.

Comments

"A Derivation of π(n) Based on a Stability Analysis of the Riemann-Zeta Function" originally appeared in Progress in Physics and is licenced under CC BY-N-ND 2.5. Copyright © 2008 Michael Harney and Ioannis Haranas.

This document is currently not available here.

Share

COinS