Traces of the Riemann zeta function on the complex plane.

[V21+1] The manuscript analyzes the traces resulting from three formulations of the Riemann zeta function. One of these formulations (hereinafter formulation (1)) does not converge, but I think I have obtained useful information, from the study of the traces that result from this formulation. 
Below, I call $a$ the real part of (s) and $b$ the imaginary part, I call formulation (1) the formulation $\zeta(s)=\sum_{n \ge 1}\frac{1}{n^s}$ 
In the manuscript I highlight that (when $b\ne0$), the divergence correspond to a spiral. 
I noticed that given a value of (s) in which $b\ne0$, the origin of the last spiral of a trace resulting from the formulation (1), always coincides with the convergence point for that given value of (s). 
The other two functions are convergent and derive from formulation (1). 
In the manuscript I mainly analyze the formulation (1), but also the most useful to understand of the other two. I also describe the reasons why I became convinced that the Riemann hypothesis is true. 
The following is a short excerpt from the manuscript that summarizes my current thinking. 
“To conclude the comparison of the three formulations, I share some considerations valid for $b\ne0$. 
The part $\displaystyle(-1)^n$, transforming the last spiral from divergent to convergent, allowed us to calculate the position of the last origin, having also become the point of convergence. Unfortunately the $\displaystyle(-1)^n$ part acts on the entire trace, moving the last origin when it does not coincide with the origin of the plane. 
It seems useful to me to know that in the traces resulting from the formulations (2) and (3), convergence point and last origin coincide. It seems useful to me to know the hidden features of the traces resulting from the formulations (1) and (3). It seems useful to me to calculate (with sufficient approximation) the position of the last origin of the traces resulting from the formulation (1)"