I will not be surprised if this question seems trivial in MO but I asked it first in MathSE and I did not get an answer. Here is the question:  

I would like to know if there is a good estimate for the sum which concerns all primes not exceeding $x$:  

$$\sum\_{p\leq x}\frac{1}{p^s}$$
with $0 < s < 1$. I have trouble bounding the sum from above. 


Thanks in advance!



prime zeta function when $0<s<1$
I will give the following 
$$\sum\_{p\leq x}\frac{1}{p^s} \approx \frac{1}{1-s}\frac{x^{1-s}}{\log x}$$
for $0\leq s < 1$ and 
$$\sum\_{p\leq x}\frac{1}{p} \approx \log \log x$$
for $s = 1$. 


