On Weierstrass Points in the Theory of Elliptic Modular Forms.
John Roderick Smart (1966)
Mathematische Zeitschrift
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John Roderick Smart (1966)
Mathematische Zeitschrift
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Matija Kazalicki, Koji Tasaka (2014)
Acta Arithmetica
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Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings. ...
Takayuki Oda (1980)
Inventiones mathematicae
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Masataka Chida (2005)
Acta Arithmetica
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Andrea Mori (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Let be an elliptic modular form level of N. We present a criterion for the integrality of at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to the iterates of the Maaß differential operators.
Salvador Comalada, Enric Nart (1992)
Mathematische Annalen
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Arjune Budhram (2002)
Acta Arithmetica
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Cremona, John E. (1997)
Experimental Mathematics
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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.
Besser, Amnon (1997)
Documenta Mathematica
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J. Hoffstein, D., Friedberg, S. Bump (1990)
Inventiones mathematicae
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D. Choi (2006)
Acta Arithmetica
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Hiraoka, Yoshio (2000)
Experimental Mathematics
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