This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
Multiplicative 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 multiplicative number theory, including not only highly general function evaluation, but also symbolic simplification.
Zeta Riemann zeta function
ZetaZero  ▪ LogIntegral  ▪ RiemannSiegelZ  ▪ PrimeZetaP  ▪ ...
Dirichlet Series
DirichletL Dirichlet L-functions
DirichletTransform Dirichlet transform of an arbitrary sequence
DirichletCharacter Dirichlet character
DivisorSigma divisor-sum function
Divisors  ▪ MoebiusMu  ▪ EulerPhi  ▪ MangoldtLambda  ▪ PrimeNu  ▪ ...
PrimePi the number of primes up to n
Prime  ▪ Mod  ▪ PowerMod  ▪ ...
DivisorSum compute a sum over divisors
DirichletConvolve Dirichlet convolution of sequences
Sum  ▪ Product  ▪ Integrate  ▪ Series  ▪ Limit