Month: August 2017

The quantity y being graphed is related to prime numbers, and the separation of the odd primes into those of the form 4k+1 and those of the form 4k+3. The non-principal Dirichlet character of period 4 can be defined by: chi(1) = 1, chi(2) = 0, chi(3) = -1, chi(4) = 0 plus the periodicity… Continue reading Graph of y = psi(x, chi), chi a non-principal Dirichlet character

On asymptotics of some large character sums. ================================================= Added Monday January 1, 2018: FOREWORD: I now consider what follows this foreword as numerical data on some large character sums. The implied asymptotic constant , 2*(exp(Euler)/Pi)^2 , is not backed by any theoretical work. I had a few email exchanges with Andrew Granville about asymptotics of… Continue reading On asymptotics of some large character sums

Today, I’m posting a variant of the PARI/gp script to solve the Lorenz system of differential equations. The use of factorials and binomial coefficients has been eliminated, so I’d expect it to run somewhat faster than the script from an earlier post.   The lorenzy4.gp PARI/gp script:   Lorenz(X0, Y0, Z0) = { order =… Continue reading An improved PARI/gp script for solving the Lorenz ODE system

At the GECCO 2017 conference in Berlin, Moalic and Gondran gave a presentation of a novel algorithm for graph coloring. The title of their presentation is: “Heuristic rope team : a parallel algorithm for graph coloring”. I made a best effort attempt to implement this in the C programming language. I was able to find… Continue reading Update on Parallel Rope Team Coloring

That’s my intention, you can ask questions, answer questions, etc. once I have this figured out. David Bernier  

The Lorenz system of differential equations is challenging to solve over extended periods of of time ‘t’, the independent variable. In “Long-Time Computability of the Lorenz System”, the authors Kehlet and Logg from Norway give a numerical solution for x(t), y(t), z(t) for t in [0, 1000] and with initial values x(0) = 1, y(0)… Continue reading PARI/gp script for Lorenz system