Some modular functions associated to the Lie algebra E8.
S.-P. Chan, M.-L. Lang, Chong-Hai Lim (1992)
Mathematische Zeitschrift
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S.-P. Chan, M.-L. Lang, Chong-Hai Lim (1992)
Mathematische Zeitschrift
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Šnobl, Libor
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Rolf Fransteiner (1990)
Mathematische Annalen
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D. Choi (2006)
Acta Arithmetica
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Besser, Amnon (1997)
Documenta Mathematica
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(2013)
Acta Arithmetica
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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 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.
Hidegoro Nakano (1968)
Studia Mathematica
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Heima Hayashi (2006)
Acta Arithmetica
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Serge Lang, Daniel S. Kubert (1978)
Mathematische Annalen
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Sung-Geun Lim (2010)
Acta Arithmetica
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