Upper bound for the height of S-integral points on elliptic curves

We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set S of places of the number field K involved, but also in terms of the degree of K, as well as the rank, the regulator and the height of a basis of the Mordell-Weil group of the curve. The proof uses the elliptic analogue of Baker's method, based on lower bounds for linear forms in elliptic logarithms.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1203.386

Valeurs algébriques de fonctions transcendantes

On étudie l'ensemble des nombres algébriques de hauteur et de degré bornés où une fonction analytique transcendante prend des valeurs algébriques. We study the set of algebraic numbers of bounded height and bounded degree where an analytic transcendental function takes algebraic value

Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach

Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

Quantitative Chevalley-Weil theorem for curves

The classical Chevalley-Weil theorem asserts that for an \'etale covering of projective varieties over a number field K, the discriminant of the field of definition of the fiber over a K-rational point is uniformly bounded. We obtain a fully explicit version of this theorem in dimension 1.Comment: version 4: minor inaccuracies in Lemma 3.4 and Proposition 5.2 correcte

Corporate reputation in the spanish context: An interaction between reporting to stakeholders and industry.

ABSTRACT: The authors describe the intensity and orientation of the corporate social responsibility (CSR) reporting in four Spanish industries and explore the relationship that exists between both concepts and an independent measurement of reputation for CSR (CSRR). The results demonstrate that the CSR reporting is especially relevant and useful in the finance industry. Finance companies report significantly more CSR information than most industries in Spain, and this reporting is more closely linked to their CSRR than the CSR reporting of basic, consumer goods and services industries. Borra

Sur le nombre de points algebriques ou une fonction analytique transcendante prend des valeurs algebriques

7 pages, submitted to C.R. Acad. Sci. ParisWe study the set of algebraic numbers of bounded height and bounded degree where an analytic transcendental function takes algebraic values