Tetragonal modular curves
Daeyeol Jeon, Euisung Park (2005)
Acta Arithmetica
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Daeyeol Jeon, Euisung Park (2005)
Acta Arithmetica
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Bruce Hunt (1990)
Compositio Mathematica
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Bumkyu Cho, SoYoung Choi, Chang Heon Kim (2013)
Acta Arithmetica
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We extend Guerzhoy's Maass-modular grids on the full modular group SL₂(ℤ) to congruence subgroups Γ₀(N) and Γ₀⁺(p).
Serge Lang, Daniel S. Kubert (1978)
Mathematische Annalen
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Alina Carmen Cojocaru, Ernst Kani (2004)
Acta Arithmetica
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Masataka Chida (2005)
Acta Arithmetica
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Arjune Budhram (2002)
Acta Arithmetica
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Nobuhiko Ishida, Noburo Ishii (2002)
Acta Arithmetica
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Shoyu Nagaoka (1997)
Manuscripta 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.
Daeyeol Jeon, Chang Heon Kim (2007)
Acta Arithmetica
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Tsz Ho Chan, Igor E. Shparlinski (2010)
Acta Arithmetica
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René Schoof, Nikos Tzanakis (2012)
Acta Arithmetica
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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.
D. Choi (2006)
Acta Arithmetica
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