%0 Journal Article
%T Modular equations for some $¦Ç$-products
%A Fran£¿ois Morain
%J Mathematics
%D 2011
%I arXiv
%X The classical modular equations involve bivariate polynomials that can be seen to be univariate with coefficients in the modular invariant $j$. Kiepert found modular equations relating some $\eta$-quotients and the Weber functions $\gamma_2$ and $\gamma_3$. In the present work, we extend this idea to double $\eta$-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.
%U http://arxiv.org/abs/1102.1606v1