Upper bounds on the heights of polynomials and rational fractions from their values
arXiv:2105.07670 · doi:10.4064/aa210816-26-1
Abstract
Let be a univariate polynomial or rational fraction of degree defined over a number field. We give bounds from above on the absolute logarithmic Weil height of in terms of the heights of its values at small integers: we review well-known bounds obtained from interpolation algorithms given values at (resp. ) points, and obtain tighter results when considering a larger number of evaluation points.
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