let [tex] \zeta(z)=\sum_{n \in \mathbb{N}} n^{-z}[/tex] ~ {{a+ib}}>1(adsbygoogle = window.adsbygoogle || []).push({});

then, [tex] \zeta(z)=0[/tex] iff z=-2n where n is a natural number.

[tex]pi(x)=\int_0^\infty\frac{dx}{\xS[x+1]} gamma(x+)[/tex]

where S[x+1]= [tex] \sum_{n \in \mathbb{N}} n^-{x+1}[/tex]

I have discovered that [tex]pi(x)=\int_a^b\frac{dx}/logx[/tex] = 1/log b+ 2/log b + 3!/logb +...

furthermore, [tex]pi(x)-\int_^x\frac{dx}[/tex]+1/2 [tex]\int_^x(1/2)\frac{dx}[/tex] (logx)^-1 ~ (x^1/3) /logx

is this already kmown ?

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# The Riemann Hypothesis

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