Minoration de la hauteur normalisée des hypersurfaces

Volume 92 / 2000

Francesco Amoroso, Sinnou David Acta Arithmetica 92 (2000), 339-366 DOI: 10.4064/aa-92-4-339-366

Abstract

1. Introduction. Dans un article célèbre, D. H. Lehmer posait la question suivante (voir [Le], §13, page 476): «The following problem arises immediately. If ε is a positive quantity, to find a polynomial of the form: $f(x) = x^r + a_1x^{r-1} + ⋯ +a_r$ where the a's are integers, such that the absolute value of the product of those roots of f which lie outside the unit circle, lies between 1 and 1 + ε (...). Whether or not the problem has a solution for ε < 0.176 we do not know.» Cette question, toujours ouverte, est la source de nombreuses conjectures: généralisation aux minimums successifs de la hauteur (ou hauteur d'un point dans $

Authors

  • Francesco Amoroso
  • Sinnou David

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