Add to ORKGAbstract. In this short note we show that the uniform abc-conjecture puts strong re-strictions on the coordinates of rational points on elliptic curves. For the proof we use a variant of Vojta’s height inequality formulated by Mochizuki. As an application, we generalize a result of Silverman on elliptic non-Wieferich primes. 1
We give bounds for the canonical height of rational and integral points on cubic twists of the Ferma...
AbstractWe estimate the bounds for the difference between the ordinary height and the canonical heig...
Let E be an elliptic curve over the rationals. A crucial step in determining a Mordell-Weil basis fo...
We combine various well-known techniques from the theory of heights, the theory of “noncritical Bel...
International audienceMost, if not all, unconditional results towards the abc-conjecture rely ultima...
Abstract. We combine various well-known techniques from the theory of heights, the theory of “noncri...
We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion r...
The paper proves uniform bounds for the number of rational points of bounded height on certain ellip...
In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geo...
We introduce the notion of height for the points on an elliptic curve, an abelian variety of genus 1...
In 2006, Mazur, Stein, and Tate gave an algorithm to compute p-adic heights and regulators on ellipt...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
This thesis deals with several theoretical and computational problems in the theory of p-adic height...
Abstract. Let C be an affine, plane, algebraic curve of degree d with integer coefficients. In 1989,...
We exhibit a genus{2 curve C de ned over Q(T ) which admits two independent morphisms to a rank{1 ...
We give bounds for the canonical height of rational and integral points on cubic twists of the Ferma...
AbstractWe estimate the bounds for the difference between the ordinary height and the canonical heig...
Let E be an elliptic curve over the rationals. A crucial step in determining a Mordell-Weil basis fo...
We combine various well-known techniques from the theory of heights, the theory of “noncritical Bel...
International audienceMost, if not all, unconditional results towards the abc-conjecture rely ultima...
Abstract. We combine various well-known techniques from the theory of heights, the theory of “noncri...
We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion r...
The paper proves uniform bounds for the number of rational points of bounded height on certain ellip...
In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geo...
We introduce the notion of height for the points on an elliptic curve, an abelian variety of genus 1...
In 2006, Mazur, Stein, and Tate gave an algorithm to compute p-adic heights and regulators on ellipt...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
This thesis deals with several theoretical and computational problems in the theory of p-adic height...
Abstract. Let C be an affine, plane, algebraic curve of degree d with integer coefficients. In 1989,...
We exhibit a genus{2 curve C de ned over Q(T ) which admits two independent morphisms to a rank{1 ...
We give bounds for the canonical height of rational and integral points on cubic twists of the Ferma...
AbstractWe estimate the bounds for the difference between the ordinary height and the canonical heig...
Let E be an elliptic curve over the rationals. A crucial step in determining a Mordell-Weil basis fo...