Document Type

Article

Department

Mathematics (CMC)

Publication Date

2006

Abstract

Let F be a non-zero polynomial with integer coefficients in N variables of degree M. We prove the existence of an integral point of small height at which F does not vanish. Our basic bound depends on N and M only. We separately investigate the case when F is decomposable into a product of linear forms, and provide a more sophisticated bound. We also relate this problem to a certain extension of Siegel’s Lemma as well as to Faltings’ version of it. Finally we exhibit an application of our results to a discrete version of the Tarski plank problem.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,295.

Source: Author's post-print manuscript in pdf.

The original publication is available at www.springerlink.com and may be found at http://www.springerlink.com/content/b6245015866546x4/?p=722bd49e5e744163b64f757264a3ad99π=2

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© 2006 Springer

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