Number Theory


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

Authors: Michael Harney, Ioannis Iraklis Haranas

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: 1 pages, Published: Progress in Physics, vol. 2, pp.8, 2010 .

Download: PDF

Submission history

[v1] 14 Feb 2010

Unique-IP document downloads: 134 times

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus