نتایج جستجو برای: mordell

تعداد نتایج: 596  

2009
P. G. Walsh P. G. WALSH

We extend a result of Spearman which provides a sufficient condition for elliptic curves of the form y2 = x3 − px, with p a prime, to have Mordell-Weil rank 2. As in Spearman’s work, the condition given here involves the existence of integer points on these curves.

2007
KEIJI OGUISO K. OGUISO

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered hyperkähler manifold. As a byproduct, we also give an explicit example of an abelian fibered variety in which the Picard number of the generic fiber in the sense of scheme is different from the Picard number of generic closed fibers.

2006
John Cremona Samir Siksek

Let E be an elliptic curve over the rationals. A crucial step in determining a Mordell-Weil basis for E is to exhibit some positive lower bound λ > 0 for the canonical height ĥ on non-torsion points. We give a new method for determining such a lower bound, which does not involve any searching for points.

2003
GANG YU

In this paper, we consider a family of elliptic curves over Q with 2-torsion part Z2. We prove that, for every such elliptic curve, a positive proportion of quadratic twists have Mordell–Weil rank 0. Mathematics Subject Classifications (2000). 11G05, 11L40, 14H52.

Journal: :Journal of Mathematical Inequalities 2018

Journal: :Journal of the American Mathematical Society 1996

Journal: :Proceedings of the Japan Academy, Series A, Mathematical Sciences 1989

Journal: :The Mathematical Intelligencer 2023

Journal: :Journal of Number Theory 2023

We applied the theory of perfectoid spaces to prove dynamical versions Manin-Mumford conjecture, Mordell-Lang and Tate-Voloch conjecture for lifts a p-th power, generalizing work Xie in [39] Frobenius.

2010
D. GHIOCA M. E. ZIEVE

The Mordell–Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of images of the origin under a finitely generated semigroup of translations. We study the analogous question in which the translations are replaced by algebraic gro...

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