/sign-changes

Code and data accompanying the paper "On the sign changes of ψ(x)-x" by M. Grześkowiak, J. Kaczorowski, Ł. Pańkowski and M. Radziejewski.

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sign-changes

This repository contains code and data accompanying the paper "On the sign changes of ψ(x)-x" by M. Grześkowiak, J. Kaczorowski, Ł. Pańkowski and M. Radziejewski, supported by the grant 2021/41/B/ST1/00241 from the National Science Centre, Poland. All the files are placed in the folder On the sign changes of ψ(x)-x.

There are two Mathematica 13.2 notebooks available also as PDF files:

  • Heuristics.nb, that shows how we searched for the best parameters,
  • Verification.nb, containing the final, rigorous computation.

The files x1.txt, ..., x21.txt, zetaZeros22.txt and zetaZeros10000.txt are needed to run the calculations in Verification.nb. In addition you can download the file

  • Presentation.nb

containing the presentation delivered in Będlewo on 23 September 2024, at the conference Analytic and Explicit results of zeros of L-functions organized by Gautami Bhowmik (Université de Lille), Anne-Maria Ernvall-Hytönen (Helsingin Yliopisto) and Łukasz Pańkowski (Adam Mickiewicz University, Poznań).