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Upper bounds on the heights of polynomials and rational fractions from their values

Volume 203 / 2022

Jean Kieffer Acta Arithmetica 203 (2022), 49-68 MSC: 11C08, 11G50. DOI: 10.4064/aa210816-26-1 Published online: 24 March 2022


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.


  • Jean KiefferMathematics Department
    Harvard University
    Cambridge, MA 02138, United States

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