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RaduRK: Ramanujan-Kolberg Program
AuthorsRaduRK 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:
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.