Geodesic
Modular equations for some $\eta $-products
François Morain1
1 INRIA Saclay–Île-de-France & Laboratoire d'Informatique (CNRS/UMR 7161) École polytechnique F-91128 Palaiseau, France
Acta Arithmetica, Tome 161 (2013) no. 4, pp. 301-326

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\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.
DOI : 10.4064/aa161-4-1
Keywords: classical modular equations involve bivariate polynomials seen univariate modular invariant integer coefficients kiepert found modular equations relating eta quotients weber functions gamma gamma present work extend idea double eta quotients characterize parameters leading kind equation properties these equations explain compute numerical examples

François Morain 1

1 INRIA Saclay–Île-de-France & Laboratoire d'Informatique (CNRS/UMR 7161) École polytechnique F-91128 Palaiseau, France 
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François Morain. Modular equations for some $\eta $-products. Acta Arithmetica, Tome 161 (2013) no. 4, pp. 301-326. doi: 10.4064/aa161-4-1

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