Mathematica supports zeta and polylogarithm functions of a complex variable in full generality, performing efficient arbitrary-precision evaluation and implementing extensive symbolic transformations.
Zeta — Riemann and generalized Riemann zeta function
ZetaZero — zeros of the zeta function on the critical line
PolyLog — ordinary and Nielsen generalized polylogarithm function
LerchPhi — Lerch function
PrimeZetaP — prime zeta function
FunctionExpand — expand out symbolic forms of functions