Modular equations for some $η$-products

Details Modular equations for some $η$-products Modular equations for some $η$-products

2011-02-08

arxiv.org/abs/1102.1606v1

Mathematics

Number Theory

Scientific paper

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.

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