This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
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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