The Wolfram Language 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

RiemannSiegelZ  ▪  RiemannSiegelTheta  ▪  StieltjesGamma  ▪  RiemannXi

ZetaZero — zeros of the zeta function on the critical line

PolyLog — ordinary and Nielsen generalized polylogarithm function

LerchPhi — Lerch function

HurwitzZeta, HurwitzLerchPhi — functions with original Hurwitz analytic structure

DirichletBeta  ▪  DirichletEta  ▪  DirichletLambda

PrimeZetaP — prime zeta function

FunctionExpand — expand out symbolic forms of functions