Hyperelliptic modular curves
Andrew P. Ogg (1974)
Bulletin de la Société Mathématique de France
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Andrew P. Ogg (1974)
Bulletin de la Société Mathématique de France
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Bruce Hunt (1990)
Compositio Mathematica
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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.
Andreas Schweizer (1997)
Collectanea Mathematica
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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.
Ernst-Ulrich Gekeler (1995)
Journal de théorie des nombres de Bordeaux
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