Modular spaces over a field with valuation generated by a (ω,ϑ)-convex modular
Ryszard Urbański (1983)
Studia Mathematica
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Ryszard Urbański (1983)
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Nobuhiko Ishida, Noburo Ishii (2002)
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Serge Lang, Daniel S. Kubert (1978)
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Roland Matthes (1996)
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Atsushi Moriwaki (1995)
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Hidegoro Nakano (1968)
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D. Choi (2006)
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Serge Lang, Daniel S. Kubert (1977)
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Dan Kubert, Serge Lang (1975)
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Besser, Amnon (1997)
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Shôzô Koshi, Tetsuya Shimogaki (1961)
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Heima Hayashi (2006)
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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.
L. Gerritzen, B. Brinkmann (1992)
Mathematische Annalen
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