Abstract.
It is proved that natural necessary conditions imply the existence of infinitely many integer points at which given multivariate polynomials with integer coefficients take coprime values. As a consequence the best constant in the simplest case of Siegel’s lemma is expressed in terms of critical determinants of suitable star bodies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received August 10, 2001; in revised form March 13, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday
Rights and permissions
About this article
Cite this article
Schinzel, A. A Property of Polynomials with an Applicationto Siegel’s Lemma. Monatsh. Math. 137, 239–251 (2002). https://doi.org/10.1007/s00605-002-0491-2
Issue Date:
DOI: https://doi.org/10.1007/s00605-002-0491-2