Arithmetic Hilbert modular functions (II).

Walter L. Baily Jr.

Displaying similar documents to “Arithmetic Hilbert modular functions (II).”

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 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.

Rings of Hilbert modular forms

E. Thomas, A. T. Vasquez (1983)

Compositio Mathematica

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Differential overconvergence

Alexandru Buium, Arnab Saha (2011)

Banach Center Publications

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We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation". This property can be viewed as a special kind of overconvergence property. One can also go in the opposite direction by using differential functions that arise in a ramified situation to construct "new" (unramified) differential functions.

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.

Modular curves and unramified extensions of number fields

S. Kamienny (1982)

Compositio Mathematica

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Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields

Chang Kim, Ja Koo (2011)

Open Mathematics

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We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.

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.