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SoYoung Choi, Chang Heon Kim (2015)
Open Mathematics
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We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.
D. Choi (2006)
Acta Arithmetica
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Besser, Amnon (1997)
Documenta Mathematica
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Hidegoro Nakano (1968)
Studia Mathematica
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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.
Heima Hayashi (2006)
Acta Arithmetica
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Özlem Imamoglu, Yves Martin (2006)
Acta Arithmetica
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Arjune Budhram (2002)
Acta Arithmetica
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Sung-Geun Lim (2010)
Acta Arithmetica
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Yichao Zhang (2011)
Acta Arithmetica
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Karen Taylor (2012)
Acta Arithmetica
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Shoyu Nagaoka (1997)
Manuscripta mathematica
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K. Ramanathan (1990)
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. ...