The Library
Root sets of polynomials and power series with finite choices of coefficients
Tools
Tools
Tools
Baker, Simon and Yu, Han (2018) Root sets of polynomials and power series with finite choices of coefficients. Computational Methods and Function Theory, 18 (1). pp. 89-97. doi:10.1007/s40315-017-0215-1
|
PDF
WRAP-root-sets-polynomials-power-series-choices-Yu-2018.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (829Kb) | Preview |
|
![[img]](http://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
Unimodular polynomials (1).pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (308Kb) |
Official URL: https://doi.org/10.1007/s40315-017-0215-1
Abstract
Given H⊆C two natural objects to study are the set of zeros of polynomials with coefficients in H,
{z∈C:∃k>0,∃(an)∈Hk+1,∑n=0kanzn=0},
and the set of zeros of a power series with coefficients in H,
{z∈C:∃(an)∈HN,∑n=0∞anzn=0}.
In this paper, we consider the case where each element of H has modulus 1. The main result of this paper states that for any r∈(1/2,1), if H is 2cos−1(5−4|r|24) -dense in S1, then the set of zeros of polynomials with coefficients in H is dense in {z∈C:|z|∈[r,r−1]}, and the set of zeros of power series with coefficients in H contains the annulus {z∈C:|z|∈[r,1)} . These two statements demonstrate quantitatively how the set of polynomial zeros/power series zeros fill out the natural annulus containing them as H becomes progressively more dense.
| Item Type: | Journal Article | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Polynomials | |||||||||
| Journal or Publication Title: | Computational Methods and Function Theory | |||||||||
| Publisher: | Heldermann Verlag | |||||||||
| ISSN: | 1617-9447 | |||||||||
| Official Date: | March 2018 | |||||||||
| Dates: |
|
|||||||||
| Date of first compliant deposit: | 2 October 2017 | |||||||||
| Volume: | 18 | |||||||||
| Number: | 1 | |||||||||
| Page Range: | pp. 89-97 | |||||||||
| DOI: | 10.1007/s40315-017-0215-1 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access | |||||||||
| Grant number: | EP/M001903/1. | |||||||||
| RIOXX Funder/Project Grant: |
|
|||||||||
| Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
