Modular equations for some η-products

Abstract

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 η-quotients and the Weber functions γ 2 and γ 3 . 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.