Displaying similar documents to “Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields”

Arithmetic of the modular function j 1 , 4

Chang Heon Kim, Ja Kyung Koo (1998)

Acta Arithmetica

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We find a generator j 1 , 4 of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator N ( j 1 , 4 ) which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.

Arithmetic Hilbert modular functions (II).

Walter L. Baily Jr. (1985)

Revista Matemática Iberoamericana

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The purpose of this paper, which is a continuation of [2, 3], is to prove further results about arithmetic modular forms and functions. In particular we shall demonstrate here a q-expansion principle which will be useful in proving a reciprocity law for special values of arithmetic Hilbert modular functions, of which the classical results on complex multiplication are a special case. The main feature of our treatment is, perhaps, its independence of the theory of abelian varieties. ...

Equations of hyperelliptic modular curves

Josep Gonzalez Rovira (1991)

Annales de l'institut Fourier

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We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.