A doubt about complex analysis

[zetafunction]

given the function

[tex] arg\xi(1/2+is) [/tex]

is this an increasing function of 's' ?? , i mean if its derivative is always bigger than 0

here xi is the Riemann Xi function

http://en.wikipedia.org/wiki/Riemann_Xi_function

could we define the 'inverse' (at least for positive s) of [tex] arg\xi(1/2+is) [/tex] ?

 

[henry_m]

I don't really know much about that function but is the whole point of it not that on 1/2+is it's real and has the same zeroes as the zeta function? In which case its argument is discontinuous and some multiple of pi the whole time.