Absolute Convergence

We tend to think that infinity must be the realm of philosophy. Our body can’t stand eternity. It is just the ideal. Riemann’s zeta function must be almost correct, but nobody can prove this difficulty because of infinity. You can see the goal, but it moves forward with you. You never reach it.
Therefore, we need to know absolute convergence to ignore infinity, but it includes complex plane.



In order to prove absolute convergence, you should accept Z=Z0 and |Z-a|＜|Z0-a|.
M must be very huge values.


(n=0.1,2....)







Then you see that |Z0-a| is the radius of the circle.
∴ |Z-a|＜|Z0-a|

This means expansion because of Σ, but it must be absolute convergence.