The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-4-1,
title = {Modular equations for some $\eta$-products},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {301-326},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-4-1}
}
(éd.). Modular equations for some η-products. Acta Arithmetica, Tome 161 (2013) pp. 301-326. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-4-1/