Ramanujan's modular equations
K. Ramanathan (1990)
Acta Arithmetica
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K. Ramanathan (1990)
Acta Arithmetica
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Sung-Geun Lim (2010)
Acta Arithmetica
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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.
Baruah, Nayandeep Deka, Saikia, Nipen (2006)
International Journal of Mathematics and Mathematical Sciences
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Masri, Riad, Ono, Ken (2009)
International Journal of Mathematics and Mathematical Sciences
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Jinhee Yi (2001)
Acta Arithmetica
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D. Choi (2006)
Acta Arithmetica
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Wissam Raji (2007)
Acta Arithmetica
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Hidegoro Nakano (1968)
Studia Mathematica
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Józef Dudek (1988)
Colloquium Mathematicae
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Baier, Harald, Köhler, Günter (2003)
Experimental Mathematics
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Heima Hayashi (2006)
Acta Arithmetica
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Chang Heon Kim, Ja Kyung Koo (1998)
Acta Arithmetica
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We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Olive C. Hazlett (1930)
Journal de Mathématiques Pures et Appliquées
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