Distribution of the traces of Frobenius on elliptic curves over function fields
Amílcar Pacheco (2003)
Acta Arithmetica
Similarity:
Amílcar Pacheco (2003)
Acta Arithmetica
Similarity:
Amílcar Pacheco (2010)
Acta Arithmetica
Similarity:
Fabien Pazuki (2014)
Publications mathématiques de Besançon
Similarity:
We compare general inequalities between invariants of number fields and invariants of elliptic curves over number fields. On the number field side, we remark that there is only a finite number of non-CM number fields with bounded regulator. On the elliptic curve side, assuming the height conjecture of Lang and Silverman, we obtain a Northcott property for the regulator on the set of elliptic curves with dense rational points over a number field. This amounts to say that the arithmetic...
M. Skałba (2005)
Acta Arithmetica
Similarity:
Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)
Acta Arithmetica
Similarity:
Takaaki Kagawa (2001)
Acta Arithmetica
Similarity:
Tomasz Jędrzejak (2012)
Colloquium Mathematicae
Similarity:
It is classical that a natural number n is congruent iff the rank of ℚ -points on Eₙ: y² = x³-n²x is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.
Lisa Berger (2012)
Acta Arithmetica
Similarity:
Horst G. Zimmer (1979)
Journal für die reine und angewandte Mathematik
Similarity:
P. G. Walsh (2009)
Acta Arithmetica
Similarity:
Ruthi Hortsch (2016)
Acta Arithmetica
Similarity:
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.
Toshiro Hiranouchi, Seiji Hirayama (2013)
Acta Arithmetica
Similarity:
Rose, Harvey E. (2000)
Experimental Mathematics
Similarity:
Nicolescu, Liviu (2005)
Balkan Journal of Geometry and its Applications (BJGA)
Similarity:
Masanari Kida (2001)
Journal de théorie des nombres de Bordeaux
Similarity:
We prove that the -invariant of an elliptic curve defined over an imaginary quadratic number field having good reduction everywhere satisfies certain Diophantine equations under some hypothesis on the arithmetic of the quadratic field. By solving the Diophantine equations explicitly in the rings of quadratic integers, we show the non-existence of such elliptic curve for certain imaginary quadratic fields. This extends the results due to Setzer and Stroeker.
Cremona, John E., Mazur, Barry (2000)
Experimental Mathematics
Similarity:
Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
Similarity:
Taras Banakh, Fedor Bogomolov, Andrij Gatalevych, Ihor Guran, Yurij Ishchuk, Mykola Komarnytskyi, Igor Kuz, Ivanna Melnyk, Vasyl Petrychkovych, Yaroslav Prytula, Oleh Romaniv, Oleh Skaskiv, Ludmyla Stakhiv, Georgiy Sullym, Bohdan Zabavskyi, Volodymir Zelisko, Mykhajlo Zarichnyi (2013)
Open Mathematics
Similarity: