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Displaying similar documents to “Determining modular forms of general level by central values of convolution L-functions”

Modular equations for some η-products

(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.

Modular parametrizations of certain elliptic curves

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. ...