Exponents for three-dimensional simultaneous Diophantine approximations

Details Exponents for three-dimensional simultaneous Diophantine approximations Exponents for three-dimensional simultaneous Diophantine approximations

2010-09-06

arxiv.org/abs/1009.0987v2

Mathematics

Number Theory

8 pages, correction of misprints, submitted to Czechoslovak Mathematical Journal

Scientific paper

Let $\Theta = (\theta_1,\theta_2,\theta_3)\in \mathbb{R}^3$. Suppose that $1,\theta_1,\theta_2,\theta_3$ are linearly independent over $\mathbb{Z}$. For Diophantine exponents $$ \alpha(\Theta) = \sup \{\gamma >0:\,\,\, \limsup_{t\to +\infty} t^\gamma \psi_\Theta (t) <+\infty \} ,$$ $$\beta(\Theta) = \sup \{\gamma >0:\,\,\, \liminf_{t\to +\infty} t^\gamma \psi_\Theta (t) <+\infty\} $$ we prove $$ \beta (\Theta) \ge {1/2} ({\alpha (\Theta)}/{1-\alpha(\Theta)} +\sqrt{{\alpha(\Theta)}/{1-\alpha(\Theta)})^2 +{4\alpha(\Theta)}/{1-\alpha(\Theta)}}) \alpha (\Theta) $$

Affiliated with

Also associated with

No associations

Rating

Exponents for three-dimensional simultaneous Diophantine approximations 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 Exponents for three-dimensional simultaneous Diophantine approximations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exponents for three-dimensional simultaneous Diophantine approximations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-297656