On values of a modular form on Γ₀(N)
D. Choi (2006)
Acta Arithmetica
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Displaying similar documents to “Generators and defining equation of the modular function field of the group Γ₁(N)”
On values of a modular form on Γ₀(N)
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Daeyeol Jeon, Euisung Park (2005)
Acta Arithmetica
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On some equalities for the Weierstrass modular units of level p
Heima Hayashi (2006)
Acta Arithmetica
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Units in the Modular Function Field. V. Iwasawa Theory in the Modular Tower.
Serge Lang, Daniel S. Kubert (1978)
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Besser, Amnon (1997)
Documenta Mathematica
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Generalized modular spaces
Hidegoro Nakano (1968)
Studia Mathematica
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Hecke action and the degree of the modular parameterization
Arjune Budhram (2002)
Acta Arithmetica
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Modular spaces over a field with valuation generated by a (ω,ϑ)-convex modular
Ryszard Urbański (1983)
Studia Mathematica
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Products of special values of modular L-functions and their applications
Masataka Chida (2005)
Acta Arithmetica
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Arithmetic of the modular function
Chang Heon Kim, Ja Kyung Koo (1998)
Acta Arithmetica
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We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
On Modular Spaces over a Field with Valuation.
Ryszard Urbanski (1986)
Mathematische Zeitschrift
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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.
On the concentration of points on modular hyperbolas and exponential curves
Tsz Ho Chan, Igor E. Shparlinski (2010)
Acta Arithmetica
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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. ...