Software

RaduRK

RaduRK is a Mathematica implementation of an algorithm developed by Cristian-Silviu Radu. The algorithm takes as input an arithmetic sequence a(n) generated from a large class of modular eta quotients, together with a given arithmetic progression mn+j, and the level of an acceptable congruence subgroup. The algorithm produces expressions for the generating function of a(mn+j) in terms of Q-linear combinations of Dedekind eta quotients which are modular over the subgroup. Identities of this form include famous results by Ramanujan which demonstrate the divisibility properties of p(5n+4) and p(7n+5). The algorithm relies on certain powerful finiteness conditions imposed by the study of modular functions, and illustrates the utility of the subject to computational number theory.

This software package was developed at the Research Institute for Symbolic Computation at Johannes Kepler University Linz, and is freely available under the terms of the GNU General Public License as published by the Free Software Foundation.

For free access to the software package and instructions for use, visit https://risc.jku.at/sw/radurk/.