Title
Polynomial Estimates, Exponential Curves and Diophantine Approximation
Document Type
Article
Date
2010
Embargo Period
9-28-2010
Keywords
Complex variables
Language
English
Disciplines
Mathematics
Description/Abstract
Abstract. Let [alpha] [is an element of] (0, 1) \ [the rationals] and K = {(ez, eaz) : |z| [less than or equal to] 1} [is a subset of] [the complex numbers]2.If P is a polynomial of degree n in [the complex numbers]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 supp ||P||[subdelta]2[is less than or equal to] exp (Cn2log n). However, for [alpha] in subset S of the Liouville numbers, supp ||P||[subdelta]2 has bigger order of growth. We give a precise characterization of the set S and study its properties.
Recommended Citation
Coman, Dan and Poletsky, Evgeny A., "Polynomial Estimates, Exponential Curves and Diophantine Approximation" (2010). Mathematics Faculty Scholarship. Paper 3.
http://surface.syr.edu/mat/3
Source
Metadata from ArXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
12 pages. To appear in Mathematical Research Letters