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Applications of the Subspace Theorem to Certain Diophantine Problems

A survey of some recent results
  • Pietro Corvahja
  • Umberto Zannier
Part of the Developments in Mathematics book series (DEVM, volume 16)

Abstract

One of the cornerstones of modern Diophantine Approximation is the Schmidt Subspace Theorem. Its original form was obtained by Wolfgang Schmidt around 1970, as an evolution of slightly special cases related to an analogue of Roth’s Theorem for simultaneous rational approximations to several algebraic numbers. While Roth’s Theorem considers rational approximations to a given algebraic point on the line, the Subspace Theorem deals with approximations to given hyperplanes in higher dimensional space, defined over the field of algebraic numbers, by means of rational points in that space.

Keywords

Diophantine approximation subspace theorem linear recurrence sequences irregular points on varieties 

2000 Mathematics subject classification

11J25 11G35 11D57 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Pietro Corvahja
    • 1
  • Umberto Zannier
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversità di UdineUdineItaly
  2. 2.Scuola Normale SuperiorePisaItaly

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