The level of distribution of the special values of L-functions
Ritabrata Munshi (2009)
Acta Arithmetica
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Ritabrata Munshi (2009)
Acta Arithmetica
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Rose, Harvey E. (2000)
Experimental Mathematics
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Amílcar Pacheco (2003)
Acta Arithmetica
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Amílcar Pacheco (2010)
Acta Arithmetica
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Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
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Cremona, John E., Mazur, Barry (2000)
Experimental Mathematics
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Gang Yu (2005)
Acta Arithmetica
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Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)
Acta Arithmetica
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Bartosz Naskręcki (2016)
Banach Center Publications
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We discuss the distribution of Mordell-Weil ranks of the family of elliptic curves y² = (x + αf²)(x + βbg²)(x + γh²) where f,g,h are coprime polynomials that parametrize the projective smooth conic a² + b² = c² and α,β,γ are elements from ℚ̅. In our previous papers we discussed certain special cases of this problem and in this article we complete the picture by proving the general results.
Lisa Berger (2012)
Acta Arithmetica
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Andrej Dujella, Kálmán Győry, Ákos Pintér (2012)
Acta Arithmetica
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Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Alf Van Der Poorten (1980)
Mémoires de la Société Mathématique de France
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Delaunay, Christophe (2001)
Experimental Mathematics
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Joseph H. Silverman, Armand Brumer (1996)
Manuscripta mathematica
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Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Ruthi Hortsch (2016)
Acta Arithmetica
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We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².
Tom Fisher (2015)
Acta Arithmetica
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We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.