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

2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-03226568
Contributor : Jean Kieffer Connect in order to contact the contributor
Submitted on : Monday, August 16, 2021 - 4:49:38 PM
Last modification on : Tuesday, October 19, 2021 - 11:06:00 PM

### Files

heights-interpolation.pdf
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### Identifiers

• HAL Id : hal-03226568, version 2
• ARXIV : 2105.07670

### Citation

Jean Kieffer. Upper bounds on the heights of polynomials and rational fractions from their values. 2021. ⟨hal-03226568v2⟩

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