On the arithmetic of certain modular curves
Daeyeol Jeon, Chang Heon Kim (2007)
Acta Arithmetica
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Daeyeol Jeon, Chang Heon Kim (2007)
Acta Arithmetica
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Serge Lang, Daniel S. Kubert (1979)
Mathematische Annalen
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X. W. C. Faber (2009)
Acta Arithmetica
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Nobuhiko Ishida, Noburo Ishii (2002)
Acta Arithmetica
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François Brunault (2008)
Acta Arithmetica
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Andreas Enge, Reinhard Schertz (2005)
Acta Arithmetica
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Daeyeol Jeon, Chang Heon Kim (2004)
Acta Arithmetica
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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.
Leprévost, Franck (1993)
Experimental Mathematics
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Yves Aubry, Marc Perret (1995)
Manuscripta mathematica
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Daeyeol Jeon, Euisung Park (2005)
Acta Arithmetica
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Gerhard Frey (1981-1982)
Groupe de travail d'analyse ultramétrique
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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.
Keisuke Arai, Fumiyuki Momose (2012)
Acta Arithmetica
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Daniel Weisser (1981)
Mathematische Annalen
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Ryszard Urbanski (1986)
Mathematische Zeitschrift
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Ki-Seng Tan, Daniel Rockmore (1992)
Journal für die reine und angewandte Mathematik
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Matija Kazalicki, Koji Tasaka (2014)
Acta Arithmetica
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Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings. ...