RaduRK

RaduRK: Ramanujan-Kolberg Program

Authors

Nicolas Smoot
RaduRK is a Mathematica implementation of Cristian-Silviu Radu's algorithm designed to compute Ramanujan-Kolberg identities. These are identities between the generating functions of certain classes of arithmetic sequences a(n), restricted to an arithmetic progression, and linear Q-combinations of eta quotients. These identities often reveal important arithmetic information about a(n). Radu's algorithm is a superb example of the utility of modular functions to computational number theory. The package has been developed by Nicolas Allen Smoot.

Licence

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses.

The package

For using the package, download the following file and put it into a directory where Mathematica will find it. For a demonstration of how to use the package see For a demonstration of the applications of the package to overpartitions, see:
  • OverpartitionExamples.nb.
For a demonstration of the applications of the package to overpartitions, see: OverpartitionExamples.nb. The package requires the following packages: 4ti2, math4ti2.m. See literature below for installation instructions.

Literature

Instructions for the proper installation for these packages and RaduRK can be found in the following paper: For details concerning the design of the algorithm, consult the following:
  • S. Radu, "An Algorithmic Approach to Ramanujan's Congruences," Ramanujan Journal, 20, pp. 215-251 (2009).
  • S. Radu, "An Algorithmic Approach to Ramanujan-Kolberg Identities," Journal of Symbolic Computation, 68, pp. 225-253 (2015).

Bugs

Please report any bugs or other suggestions to Nicolas Smoot.