Riemann Zeta Function
It's an analytic continuation of the complex function along with its derivatives whose Normal functions tends to converge when the value of ζ>1 but when ζ<1 then the functions try to continue infinitely with "Trivial Zeros" at the even negative points and wherever the complex function is achieved then the complex extends in a beautiful angle preserving way towards the Complex plans before coming to an abrupt stop.
Functions like this are called "The Symphony of the Primes".....
Zeta can take any value.... Any value either simple or complex & represented as the function of this value.
(1/2)^2 is easy to find.
But...
(1/2)^2+i is somewhat difficult. It can be splits up in (1/2)^2 * (1/2)^i...
(1/2)^2 has a value of (1/4)
But...
(1/2)^i has been a unit circle with a complex plane. When both the functions are merged then the (1/4) forms a diagonal line or radius over the unit circle.
The Zeta function is defined as...
ζ(S) = S^2 ζ'(S) = 2S
ζ(X + i) =......... What value is required to make the complex function 0.
ζ(s) = 1/1^s + 2/2^s +3/3^s.....
ζ(s + i) = 1/1^s+1+ 2/2^s+2 +3/3^s+3....
ζ can be expressed as the function of any values with the complex part coming to a abrupt stop along with the single part continuing through a analytic continuation.
But when will the ζ function be 0... Well, it is 0 in -2, -4, -6, -8..... But which is the last point where the ζ abruptly stopped in the simple plane.
