Products of special values of modular L-functions and their applications
Masataka Chida (2005)
Acta Arithmetica
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Masataka Chida (2005)
Acta Arithmetica
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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. ...
Besser, Amnon (1997)
Documenta Mathematica
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D. Choi (2006)
Acta Arithmetica
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Daeyeol Jeon, Euisung Park (2005)
Acta Arithmetica
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J. Hoffstein, D., Friedberg, S. Bump (1990)
Inventiones mathematicae
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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.
Hidegoro Nakano (1968)
Studia Mathematica
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Nobuhiko Ishida, Noburo Ishii (2002)
Acta Arithmetica
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Heima Hayashi (2006)
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.
Özlem Imamoglu, Yves Martin (2006)
Acta Arithmetica
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Hiraoka, Yoshio (2000)
Experimental Mathematics
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Sung-Geun Lim (2010)
Acta Arithmetica
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