[math-fun] infinitary Zeta

hi all, could anyone point me to a low-level text about Zeta functions? I'd like to play with the idea that since Sum( k=1..inf; mu(k)/k^w) = 1/Zeta(w) , an infinitary iZeta(w) could be defined by iZeta(w) = 1/Sum( k=1..inf; imu(k)/k^w) where imu(k) is the infinitary Moebius function A064179 (same as mu(k), except its zero's are turned into +1 or -1 depending on the sum of the binary digits over all prime exponents of k being even or odd). What properties of Zeta would be conserved in this iZeta ? Is iZeta(1) = inf ??? Wouter.