Davenport-Schmidt theorem

For any real ξ which is not rational or quadratic irrational, there are infinitely many rational or real quadratic irrational α which satisfy




C0 is any fixed number greater than 1609 and H(α) is the of α.[DS]
The of the rational or quadratic irrational number α is


where x,y,z are from the unique equation


such that x,y,z are not all zero relatively prime integral coefficients.[DS]


  • DS Davenport, H. Schmidt, M. Wolfgang: Approximation to real numbers by quadratic irrationals. Acta Arithmetica XIII, 1967.
Title Davenport-Schmidt theorem
Canonical name DavenportSchmidtTheorem
Date of creation 2013-03-22 13:32:58
Last modified on 2013-03-22 13:32:58
Owner Daume (40)
Last modified by Daume (40)
Numerical id 9
Author Daume (40)
Entry type Theorem
Classification msc 11J68