A part is everything

It is very difficult to see what Riemann's zeta function is. I don't write about 0 and I can't understand it. However, it is connected with prime numbers.

Now I got this formula.
logζ(s)=1/2^s+(1/2*1/2^2s)+(1/3*1/2^3s)+・・+1/3^s+(1/2*1/3^2s)+(1/3*1/3^3s)+・・1/5^s+(1/2*1/5^2s)+(1/3*1/5^3s)+・・・

Then, you pick up (1/2*1/3^2s) from it. I don't know the reason, but I follow Prime obsession.

I can't understand this process, but this leads to J function

You may see a form which is almost a rectangular (width="3^2→∞", height="1/2").

J(x) include ∞, and 1/2*s*∫[3^2→∞]x^(-s-1)dx is also ∞.
Is this like a black hole?