RHpack Home Page

Introduction:

These are instructions for obtaining the software RHpack.m, a Mathematica package of functions which goes with "Equivalents of the Riemann hypothesis: Volume One, Arithmetic Equivalents", by Kevin A. Broughan published by Cambridge University Press. There are more details concerning the package, its installation and functions in the "RHpack mini-manual", which is included in the book as Appendix B, page 294.

To use the software having Mathematica version 10.0 or later is recommended. Since the software is in the form of a standard mathematica package, it should run under any operating system (Windows, MacOS, Unix/Linux).

Requests for assistance and advice are welcome, as are bug reports and suggestions for new software. If you find RHpack useful please let me know, and give references for any published work which references the software. The email address is given below.

The Functions of RHpack:

AllPrimesFactor, BacklundB, CAPrimes, CheckCNk, ColossallyAbundantF, ColossallyAbundantInteger, ColossallyAbundantQ, CompositeQ, ComputeC, ComputeDeltas, Computef, ComputeH, ComputeKm, ComputeTheta, ComputeThetaValues, CriticalEpsilonValues, DivisibilityGraph, ExtraordinaryQ, ExtremelyAbundantQ, FareyFractions, FHalf, FindNextXA, GenerateCA, GenerateHC, GenerateHR, GenerateLandau, GenerateSA, GronwallG, HardyRamanujanQ, HardyRamanujanToPrimorialForm, HighlyCompositeQ, InitialCA, InitialCAPrimes, InitialCA150, InitialHC, InitialLandau, InitialSA, InitialSA1000, InitialNR, InitialXA, IntegerHeight, KFreeQ, KthApproximatePrimorial, KthPrimorial, LagariasInequalityQ, Lambda, LargestZetaZero, LeftAbundantQ, LogKthPrimorialBounds, M, MaxPrime, NextZetaZero, NiceFactorInteger, NicolasInequalityQ, NicolasTwoFailures, NOverPhi, NthHarmonicNumber, NthPrime, NthPrimeBounds, PlotCNk, PlotDivisibilityGraph, PlotEulerPhiRatio, PlotRobinsInequality, PlotVonMangoldtPsi, PowerfulQ, PrimePower, PrimorialFormQ, PrimorialFormToInteger, Psi, Psi0, PsiLargeXEpsilon, PsiLargeXEpsilon2, PsiSmallXEpsilon, RedhefferMatrix, RightAbundantQ, RobinsInequalityQ, S, SetA, SetB, SetC, SetD, SigmaOverN, SuperAbundantQ, UnitaryDivisorSigma, VerifyThetaX, Xi, ZetaZeroCount, ZetaZeroHeight.

RHpack errata:

Page references are to Appendix B of Equivalents of the Riemann Hypothesis, vol. One: Arithmetic Equivalents, CUP (2017).
  • p298 line 1: CompositeQ is now a Mathematica function, but the abbreviation coq still works
  • p303 line 13: InitialSA1000 → InitialSA100, 1000 → 100
  • p303 line 19: increasing → non-increasing
  • p309 line 1: pfq → prq

    To obtain a copy of RHpack.m send an email request to broughan.kevin@gmail.com with RHpack.m in the title.

    Last modified: 29th March 2024.