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 .

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Submission history

[v1] 14 Feb 2010

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