Winding quotients and some variants of Fermat's Last Theorem.
Henri Darmon, Loic Merel (1997)
Journal für die reine und angewandte Mathematik
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Henri Darmon, Loic Merel (1997)
Journal für die reine und angewandte Mathematik
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François Brunault (2008)
Acta Arithmetica
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Daeyeol Jeon, Chang Heon Kim (2004)
Acta Arithmetica
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Andreas Enge, Reinhard Schertz (2005)
Acta Arithmetica
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Ki-Seng Tan, Daniel Rockmore (1992)
Journal für die reine und angewandte Mathematik
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Pilar Bayer (2002)
Banach Center Publications
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We present an approach to the uniformization of certain Shimura curves by means of automorphic functions, obtained by integration of non-linear differential equations. The method takes as its starting point a differential construction of the modular j-function, first worked out by R. Dedekind in 1877, and makes use of a differential operator of the third order, introduced by H. A. Schwarz in 1873.
Daeyeol Jeon, Euisung Park (2005)
Acta Arithmetica
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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. ...
S. Kamienny (1985)
Journal für die reine und angewandte Mathematik
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Cremona, John E. (1997)
Experimental Mathematics
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Glenn Stevens (1989)
Inventiones mathematicae
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Daeyeol Jeon, Chang Heon Kim (2007)
Acta Arithmetica
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J. E. Cremona (1993)
Journal de théorie des nombres de Bordeaux
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In this note we extend the computations described in [4] by computing the analytic order of the Tate-Shafarevich group III for all the curves in each isogeny class ; in [4] we considered the strong Weil curve only. While no new methods are involved here, the results have some interesting features suggesting ways in which strong Weil curves may be distinguished from other curves in their isogeny class.
G. Frey (1982)
Journal für die reine und angewandte Mathematik
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Jing Yu (1980)
Mathematische Annalen
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Serge Lang, Daniel S. Kubert (1979)
Mathematische Annalen
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P. Monsky (1996)
Mathematische Zeitschrift
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