Modular equations for some $\eta$-products
Number Theory
2011-02-09 v1
Abstract
The classical modular equations involve bivariate polynomials that can be seen to be univariate with coefficients in the modular invariant . Kiepert found modular equations relating some -quotients and the Weber functions and . In the present work, we extend this idea to double -quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.
Cite
@article{arxiv.1102.1606,
title = {Modular equations for some $\eta$-products},
author = {François Morain},
journal= {arXiv preprint arXiv:1102.1606},
year = {2011}
}