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Paper detail

Modular equations for some $η$-products

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.

preprint2011arXivOpen access
François Morain
math.NT
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François Morain

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