On simultaneous rational approximations to a real number, its square, and its cube

Details On simultaneous rational approximations to a real number, its square, and its cube On simultaneous rational approximations to a real number, its square, and its cube

2007-12-14

arxiv.org/abs/0712.2304v2

Mathematics

Number Theory

12 pages

Scientific paper

We provide an upper bound on the uniform exponent of approximation to a triple (xi, xi^2, xi^3) by rational numbers with the same denominator, valid for any transcendental real number xi. This upper bound refines a previous result of Davenport and Schmidt. As a consequence, we get a sharper lower bound on the exponent of approximation of such a number xi by algebraic integers of degree at most 4.

Affiliated with

Also associated with

No associations

Rating

On simultaneous rational approximations to a real number, its square, and its cube 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 On simultaneous rational approximations to a real number, its square, and its cube, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On simultaneous rational approximations to a real number, its square, and its cube will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-662347