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.

ReferenceReference

Zeta Functions »

Zeta Riemann zeta function

ZetaZero ▪ LogIntegral ▪ RiemannSiegelZ ▪ PrimeZetaP ▪ ...

Dirichlet Series

DirichletL Dirichlet L-functions

DirichletTransform Dirichlet transform of an arbitrary sequence

Arithmetic Functions »

DirichletCharacter Dirichlet character

DivisorSigma divisor-sum function

Divisors ▪ MoebiusMu ▪ EulerPhi ▪ MangoldtLambda ▪ PrimeNu ▪ ...

Prime Numbers »

PrimePi the number of primes up to

Prime ▪ Mod ▪ PowerMod ▪ ...

Operations

DivisorSum compute a sum over divisors

DirichletConvolve Dirichlet convolution of sequences

Sum ▪ Product ▪ Integrate ▪ Series ▪ Limit

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