Approximation to Real Numbers by Cubic Algebraic Integers I
By Damien Roy. 2002
101 citations recorded by the source corpus.
In 1969, H. Davenport and W. M. Schmidt studied the problem of approximation to a real number ξ by algebraic integers of degree at most 3. They did so, using geometry of numbers, by resorting to the dual problem of finding simultaneous approximations to ξ and ξ2 by rational numbers with the same denominator. In this paper, we show that their measure of approximation for the dual problem is optimal and that it is realized for a countable set of real numbers ξ. We give several properties of these numbers including measures of approximation by rational numbers, by quadratic real numbers and by algebraic integers of degree at most 3. 2000 Mathematics Subject Classification 11J04 (primary), 11J13, 11J82 (secondary).
Subfields: Artificial Intelligence, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/a0b86b5efe9885722bf57df6085db654b0a1646d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
In Computational Theory and Mathematics
Citations in the corpus
- On Exponents of Homogeneous and Inhomogeneous Diophantine Approximation (2005, background): “In view of the results of [40], [39], [8], it may be possible to determine the Hausdorff dimensions of the sets Uw(A) and Uw(A), when A = (ξ, ξ(2)) and ξ is a Sturmian continued fraction.”
- On transfer inequalities in Diophantine approximation (2007, background): “See the articles [5, 13, 18, 19] and the reports [2, 20] for relating those exponents with various results on algebraic approximation.”