Polynomial estimates, exponential curves and Diophantine approximation

Details Polynomial estimates, exponential curves and Diophantine approximation Polynomial estimates, exponential curves and Diophantine approximation

2010-09-22

arxiv.org/abs/1009.4408v1

Mathematics

Complex Variables

12 pages. To appear in Mathematical Research Letters

Scientific paper

Let $\alpha\in(0,1)\setminus{\Bbb Q}$ and $K=\{(e^z,e^{\alpha z}):\,|z|\leq1\}\subset{\Bbb C}^2$. If $P$ is a polynomial of degree $n$ in ${\Bbb C}^2$, normalized by $\|P\|_K=1$, we obtain sharp estimates for $\|P\|_{\Delta^2}$ in terms of $n$, where $\Delta^2$ is the closed unit bidisk. For most $\alpha$, we show that $\sup_P\|P\|_{\Delta^2}\leq\exp(Cn^2\log n)$. However, for $\alpha$ in a subset ${\mathcal S}$ of the Liouville numbers, $\sup_P\|P\|_{\Delta^2}$ has bigger order of growth. We give a precise characterization of the set ${\mathcal S}$ and study its properties.

Affiliated with

Also associated with

No associations

Rating

Polynomial estimates, exponential curves and Diophantine approximation 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 Polynomial estimates, exponential curves and Diophantine approximation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polynomial estimates, exponential curves and Diophantine approximation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-638352