Diophantine Approximation and Integral Points on Curves

  • Marc Hindry
  • Joseph H. Silverman
Part of the Graduate Texts in Mathematics book series (GTM, volume 201)

Abstract

The fundamental problem in the subject of Diophantine approximation is the question of how closely an irrational number can be approximated by a rational number. For example, if α ∈ ℝ is any given real number, we may ask how closely can one approximate α by a rational number p/q ∈ ℚ The obvious answer is that the difference (p/q) — α∣ can be made as small as desired by an appropriate choice of p/q. This is nothing more than the assertion that ℚ is dense in ℝ. The problem is to show that if the difference is small, then p and q must be large.

Keywords

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Marc Hindry
    • 1
  • Joseph H. Silverman
    • 2
  1. 1.Département de MathématiquesUniversité Denis Diderot Paris 7ParisFrance
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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