2011/02/08 by François Morain, Morain, François
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1102.1606
arxiv created 2011/02/08 · arxiv updated 2011/02/09
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 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.