On values of a modular form on Γ₀(N)
D. Choi (2006)
Acta Arithmetica
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D. Choi (2006)
Acta Arithmetica
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Besser, Amnon (1997)
Documenta Mathematica
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J. Hoffstein, D., Friedberg, S. Bump (1990)
Inventiones mathematicae
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Kenneth A. Ribet (1976)
Inventiones mathematicae
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Hidegoro Nakano (1968)
Studia Mathematica
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Heima Hayashi (2006)
Acta Arithmetica
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Benedict H. Gross, Kevin Keating (1993)
Inventiones mathematicae
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Anatolii N. Andrianov (1979)
Inventiones mathematicae
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G. van der Geer (1982)
Mathematische Annalen
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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.
Sung-Geun Lim (2010)
Acta Arithmetica
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K.A. Ribet (1990)
Inventiones mathematicae
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