Integral Points of Small Height Outside of a Hypersurface

• Autores: Lenny Fukshansky
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 147, Nº 1, 2006, págs. 25-41
• Idioma: inglés
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• Resumen

  • 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.