Upper bounds on the heights of polynomials and rational fractions from their values
Résumé
Let F be a univariate polynomial or rational fraction of degree d defined over a number field. We give bounds from above on the absolute logarithmic Weil height of F in terms of the heights of its values at small integers: we review well-known bounds obtained from interpolation algorithms given values at d+1 (resp. 2d+1) points, and obtain tighter results when considering a larger number of evaluation points.
Domaines
Théorie des nombres [math.NT]Origine | Fichiers produits par l'(les) auteur(s) |
---|