## 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:** 124 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.*

*
*