Displaying similar documents to “Modular embeddings for some non-arithmetic Fuchsian groups”

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.

Special values of Hilbert modular functions.

Martin L. Karel (1986)

Revista Matemática Iberoamericana

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Recently, Baily has established new foundation for complex multiplication in the context of Hilbert modular functions; see [1]-[4]. However, in his treatment there is a restriction on the class of CM-points treated. Namely, the order of complex multiplications associated to the point must be the maximal order in its quotient field. The purpose of this paper is two-fold: (1) to remove the restriction just mentioned; (2) to recover a result of Tate on the conjugates of CM-points by arbitrary...

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. ...

An integrality criterion for elliptic modular forms

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 f be an elliptic modular form level of N. We present a criterion for the integrality of f at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to f the iterates of the Maaß differential operators.