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.

ReferenceReference

Zeta Functions »

Zeta Riemann zeta function

PrimeZetaP prime zeta function

HurwitzZeta ▪ LerchPhi ▪ RiemannSiegelZ ▪ ZetaZero ▪ ...

Dirichlet Functions

DirichletL Dirichlet L-function

DirichletCharacter ▪ DirichletTransform ▪ DirichletConvolve ▪ DivisorSum

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

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