Displaying similar documents to “Orthogonal polynomials and enumeration problems in molecular biology. (Polynômes orthogonaux et problèmes d'énumération en biologie moléculaire.)”

Minoration de la hauteur normalisée des hypersurfaces

Francesco Amoroso, Sinnou David (2000)

Acta Arithmetica

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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 1 x 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,...