Upper bounds on the heights of polynomials and rational fractions from their values
Volume 203 / 2022
Acta Arithmetica 203 (2022), 49-68
MSC: 11C08, 11G50.
DOI: 10.4064/aa210816-26-1
Published online: 24 March 2022
Abstract
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.
