Given the function,

$\displaystyle \zeta (M,s)=\zeta (x)\prod_{p\leq M}(1-\frac{1}{p^{s}})$

where the product is taken over primes $\displaystyle p$.

How do you find the asymptotic relation

$\displaystyle \ln \zeta (7,s)\sim \frac{1}{11^{s}}$

Thanks