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