Can Riemann zeta function be written as ##f(s)=u(s)+iv(s)##?

[Adel Makram]

I don't recall that I have seen Riemann zeta function put in the form of $f(s)=u(s)+iv(s)$.

 

[mfb]

Every complex-valued function can be written that way, but that doesn't mean it has to be useful.