Integral Points of Small Height Outside of a Hypersurface |
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Authors: | Lenny Fukshansky |
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Institution: | (1) Texas A&M University, College Station, TX, USA |
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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. |
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Keywords: | 2000 Mathematics Subject Classifications: 11C08 11H06 11D04 11H46 |
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