This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
Analytic Number Theory
Building on its broad strengths in mathematics in general, and in special functions in particular, Mathematica provides a unique level of support for analytic number theory, including not only highly general function evaluation, but also symbolic simplification.
Zeta Riemann zeta function
PrimeZetaP prime zeta function
HurwitzZeta  ▪ LerchPhi  ▪ RiemannSiegelZ  ▪ ZetaZero  ▪ ...
Dirichlet Functions
DirichletL Dirichlet L-function
PrimePi prime counting function
Prime the n^(th) prime number
NextPrime  ▪ RiemannR  ▪ PrimeOmega  ▪ PrimeNu  ▪ MangoldtLambda  ▪ ...
DivisorSigma  ▪ MoebiusMu  ▪ EulerPhi  ▪ ...
Log  ▪ Gamma  ▪ LogGamma  ▪ LogIntegral  ▪ ...