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

Bosser, Vincent and Surroca, Andrea. (2014) Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture. Bulletin of the Brazilian Mathematical Society, 45 (1). pp. 1-23.

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Official URL: http://edoc.unibas.ch/dok/A6165152

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Abstract

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 anew 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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
UniBasel Contributors:Surroca, Andrea
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:Springer
ISSN:1678-7544
e-ISSN:1678-7714
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:05 Oct 2017 14:43
Deposited On:13 Sep 2013 07:52

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