[1] **viXra:1002.0024 [pdf]**
*submitted on 14 Feb 2010*

**Authors:** Michael Harney, Ioannis Iraklis Haranas

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

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.

**Category:** Number Theory