Approximation to real numbers by cubic algebraic integers I

Details Approximation to real numbers by cubic algebraic integers I Approximation to real numbers by cubic algebraic integers I

2002-10-11

arxiv.org/abs/math/0210181v2

Proc. London Math. Soc. 88 (2004), 42-62

Mathematics

Number Theory

22 pages, v2: minor corrections

Scientific paper

In 1969, H. Davenport and W. M. Schmidt studied the problem of approximation to a real number \xi by algebraic integers of degree at most three. They did so, using geometry of numbers, by resorting to the dual problem of finding simultaneous approximations to \xi and \xi^2 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 \xi. 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 three.

Affiliated with

Also associated with

No associations

Rating

Approximation to real numbers by cubic algebraic integers I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximation to real numbers by cubic algebraic integers I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximation to real numbers by cubic algebraic integers I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-372489