Exact Russell-Type Modular Equations
Number Theory
2016-08-08 v1
Abstract
This paper provides some statistics for the coefficients of Russell- Type modular equations for the modular function, {\lambda}({\tau}). The results hold uniformly for all odd primes. They do not rely on any numerical evaluations of coefficients of q expansions of {\lambda}. The method relies on an internal structure of the coefficients of {\lambda} expressed in terms of multiplicative functions defined on integer partitions. The method may be extended to other types of modular equations.
Cite
@article{arxiv.1608.01765,
title = {Exact Russell-Type Modular Equations},
author = {Timothy Redmond and Charles Ryavec},
journal= {arXiv preprint arXiv:1608.01765},
year = {2016}
}