Building on its broad strengths in mathematics in general, and in special functions in particular, the Wolfram Language provides a unique level of support for analytic number theory, including not only highly general function evaluation, but also symbolic simplification.

Zeta Functions »

Zeta — Riemann zeta function

PrimeZetaP — prime zeta function

HurwitzZeta  ▪  LerchPhi  ▪  RiemannSiegelZ  ▪  ZetaZero  ▪  ...

Dirichlet Functions

DirichletL — Dirichlet L-function

DirichletCharacter  ▪  DirichletTransform  ▪  DirichletConvolve  ▪  DivisorSum

DirichletBeta  ▪  DirichletEta  ▪  DirichletLambda

RamanujanTau  ▪  RamanujanTauL  ▪  RamanujanTauZ  ▪  RamanujanTauTheta

Distribution of Primes »

PrimePi — prime counting function

Prime — the n ^th prime number

NextPrime  ▪  RiemannR  ▪  PrimeOmega  ▪  PrimeNu  ▪  MangoldtLambda  ▪  ...

Arithmetic and Analytic Functions »

DivisorSigma  ▪  MoebiusMu  ▪  EulerPhi  ▪  ...

Log  ▪  Gamma  ▪  LogGamma  ▪  LogIntegral  ▪  ...

Operations

Sum  ▪  Product  ▪  Integrate  ▪  Series  ▪  FourierSequenceTransform