Zobrazeno 1 - 10
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pro vyhledávání: '"11G05, 11A41"'
Autor:
Garnek, Jędrzej
Publikováno v:
International Journal of Number Theory, 2018
In this note we investigate the $p$-degree function of elliptic curves over the field $\mathbb{Q}_p$ of $p$-adic numbers. The $p$-degree measures the least complexity of a non-zero $p$-torsion point on an elliptic curve. We prove some properties of t
Externí odkaz:
http://arxiv.org/abs/1701.08822
Autor:
Voutier, Paul, Yabuta, Minoru
Publikováno v:
Acta Arith. 151 (2012), 165-190
Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$. We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is odd with $x(P)<0$ or $x(P)$ a perfect square, then the $n$-th element of the elliptic divisibi
Externí odkaz:
http://arxiv.org/abs/1009.0872
Autor:
Everest, Graham, Ward, Thomas
Publikováno v:
Amer. Math. Monthly 118(7), 584-598 (2011)
Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a non-singular plane cubic equation has
Externí odkaz:
http://arxiv.org/abs/1005.0315
On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. We prove that the number of prime terms in the sequence is uniformly bounded. When the rational point i
Externí odkaz:
http://arxiv.org/abs/1003.2131
An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rational numbers, assuming Lang's conjecture, and over the rationa
Externí odkaz:
http://arxiv.org/abs/0712.2696
We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u^3+v^3=m, with m cube-free, all the terms beyond the first have a primitive divisor.
Comment: 33 pages, 4 figures
Comment: 33 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/math/0703553
Autor:
Jędrzej Garnek
In this note we investigate the $p$-degree function of elliptic curves over the field $\mathbb{Q}_p$ of $p$-adic numbers. The $p$-degree measures the least complexity of a non-zero $p$-torsion point on an elliptic curve. We prove some properties of t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db5b218c8b16bf0c2640a236f0273e36
http://arxiv.org/abs/1701.08822
http://arxiv.org/abs/1701.08822
Autor:
Garnek, J��drzej
In this note we investigate the $p$-degree function of elliptic curves over the field $\mathbb{Q}_p$ of $p$-adic numbers. The $p$-degree measures the least complexity of a non-zero $p$-torsion point on an elliptic curve. We prove some properties of t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::122324dfd97c98f75e480687af943cda
Autor:
Paul Voutier, Minoru Yabuta
Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$. We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is odd with $x(P)
version accepted for publication. Difference of heights result moved to ht
version accepted for publication. Difference of heights result moved to ht
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6db49aaeb8e54f892d1f1a33456dec0
An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rational numbers, assuming Lang's conjecture, and over the rationa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::502d9d31805895b91c8d5da2d6177670