# Tagged Questions

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### Is it true that $\gamma_{\lfloor\log\Gamma(x)\rfloor}\sim 2\pi x$?

I realise that Gram points can approximate the imaginary part on the $x$th zeta zero $(\gamma_x)$ accurately, and indeed, Guilherme França, André LeClair give another formula, namely ...
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### On the sum of prime powers

Has anybody investigated the asymptotic growth rate of functions in the form of $$f(z,n)=\sum\limits_{p\le n}p^z$$ For $Re(z)\ge -1$. Of course $f(0,n)=\pi (n)$ has an ocean of research surrounding ...
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### Asymptotics for Mertens function

It seems that the cumulative mean of the Mertens function is very similar in behaviour to $x$ raised to the power of the first zeta zero. I tentatively notate it as: ...
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### prime zeta function when $0<s<1$ [duplicate]

I would like to know if there is a good estimate for the sum which concerns all primes not exceeding $x$: $$\sum\limits_{p\leq x}\frac{1}{p^s}$$$$0<s<1$$. Only this. Thanks in advance!
### Why is $\pi$ the Limit of the Absolute Value of the Prime $\zeta$ Function?
Motivation: I was looking at the approximation of the truncated Prime $\zeta$ function $$P_x(s)=\sum_{p\leq x}p^{-s}= \mathrm{li}(x^{1-s}) + O \left(\cdot \right)$$ (to be found here with or ...
### Approximation of Products of Truncated Prime $\zeta$ Functions
The problem arose, while I was looking at products of power prime zeta functions $$P_x(ks)=\sum_{p\,\in\mathrm{\,primes}\leq x} p^{-ks},$$ with $k\in \mathbb{N}$ and $s=it$ with real $t$. By using ...