Approximation to real numbers by cubic algebraic integers . II

  title={Approximation to real numbers by cubic algebraic integers . II},
  author={Damien Roy},
It has been conjectured for some time that, for any integer n ≥ 2, any real number ε > 0 and any transcendental real number ξ, there would exist infinitely many algebraic integers α of degree at most n with the property that |ξ−α| ≤ H(α)−n+ε, where H(α) denotes the height of α. Although this is true for n = 2, we show here that, for n = 3, the optimal exponent of approximation is not 3 but (3 + √ 5)/2 2.618. 
Highly Influential
This paper has highly influenced 14 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-9 of 9 references

Diophantine Approximation

  • W. M. Schmidt
  • Lecture Notes in Math. 785, Springer- Verlag, New…
  • 2002

Zamboni , Transcendence of Sturmian or morphic continued fractions

  • J. L. Davison, M. Queffélec, Q. L.
  • J . Number Theory
  • 2001

Approximation to real numbers by algebraic integers

  • W. M. Schmidt H. Davenport
  • Acta Arith .
  • 1969

Approximation to real numbers by quadratic irrationals

  • H. Davenport, W. M. Schmidt
  • Acta Arith. 13
  • 1967
1 Excerpt

Approximation d ’ un nombre réel par des nombres algébriques de degré donné

  • O. Teulié Y. Bugeaud
  • Acta Arith .