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.

Additional Information

12 pages. To appear in Mathematical Research Letters

Source

Metadata from ArXiv.org

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.