Calculation of the Zeros of the Riemann Zeta Function

This program can calculate the number of non-trivial roots of the Riemann Zeta Function for a given imaginary interval [a,b] and show an explicit list of which they are. It can also show a list with the imaginary part from the n-th root to the m-th root.

Installation

To get the repository type in a terminal

git clone https://github.com/julian20250/RiemannZetaZeros.git

Needed Libraries

• Boost.

  In order to calculate the Bernoulli numbers, this library is needed. To install it, download the last version https://www.boost.org/users/download/ and unpack its contents in the libraries/ directory of this project.

• Click.

  To execute the programs you need click. It can be easily installed with pip.

  pip install click

Usage

There are two main scripts: find_roots.py and nm_roots.py. The documentation of each one can be accessed writing

python find_roots.py --help

or

python nm_roots.py --help

find_roots.py finds the number of roots with imaginary part in a given interval [a,b] and nm_roots.py prints a list with the imaginary part from the n-th root to the m-th root. The first script can be parallelized in order to increase the execution speed. For more information refer to the documentation of each script.

Don't be alarmed if the execution of these scripts creates directories or .out files. They'll be removed after the execution of these scripts. If the script is stopped, these files won't be erased, but they won't prevent the execution of the scripts, so you don't need to manually remove them to avoid problems.