Generators and defining equation of the modular function field of the group Γ₁(N)
Nobuhiko Ishida, Noburo Ishii (2002)
Acta Arithmetica
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Nobuhiko Ishida, Noburo Ishii (2002)
Acta Arithmetica
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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.
Takashi Fukuda, Keiichi Komatsu (2003)
Journal de théorie des nombres de Bordeaux
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Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field of modulo . Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group for the special values. Futhermore we construct the full unit group of using modular and circular units under the GRH.
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 be an elliptic modular form level of N. We present a criterion for the integrality of at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to the iterates of the Maaß differential operators.
Bruce Hunt (1990)
Compositio Mathematica
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K. Ramanathan (1990)
Acta Arithmetica
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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. ...
D. Choi (2006)
Acta Arithmetica
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Besser, Amnon (1997)
Documenta Mathematica
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