English

Modular equations for some $\eta$-products

Number Theory 2011-02-09 v1

Abstract

The classical modular equations involve bivariate polynomials that can be seen to be univariate with coefficients in the modular invariant jj. Kiepert found modular equations relating some η\eta-quotients and the Weber functions γ2\gamma_2 and γ3\gamma_3. In the present work, we extend this idea to double η\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.

Keywords

Cite

@article{arxiv.1102.1606,
  title  = {Modular equations for some $\eta$-products},
  author = {François Morain},
  journal= {arXiv preprint arXiv:1102.1606},
  year   = {2011}
}
R2 v1 2026-06-21T17:23:18.592Z