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Root sets of polynomials and power series with finite choice of coefficients
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dc.contributor.author | Baker, Simon | |
dc.contributor.author | Yu, Han | |
dc.date.accessioned | 2017-10-10T10:30:18Z | |
dc.date.available | 2017-10-10T10:30:18Z | |
dc.date.issued | 2018-03 | |
dc.identifier.citation | Baker , S & Yu , H 2018 , ' Root sets of polynomials and power series with finite choice of coefficients ' , Computational Methods and Function Theory , vol. 18 , no. 1 , pp. 89-97 . https://doi.org/10.1007/s40315-017-0215-1 | en |
dc.identifier.issn | 1617-9447 | |
dc.identifier.other | PURE: 251080462 | |
dc.identifier.other | PURE UUID: b272abf6-cd6d-4ee8-ba50-d4910716d1cc | |
dc.identifier.other | Scopus: 85042224867 | |
dc.identifier.other | WOS: 000425363600005 | |
dc.identifier.uri | https://hdl.handle.net/10023/11822 | |
dc.description | The first author is supported by the EPSRC Grant EP/M001903/1. The second author is supported by a PhD scholarship provided by the School of Mathematics in the University of St Andrews. | en |
dc.description.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. | |
dc.format.extent | 9 | |
dc.language.iso | eng | |
dc.relation.ispartof | Computational Methods and Function Theory | en |
dc.rights | © The Author(s) 2017. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | en |
dc.subject | Root set | en |
dc.subject | Littlewood polynomials | en |
dc.subject | Unimodular polynomials | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Root sets of polynomials and power series with finite choice of coefficients | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1007/s40315-017-0215-1 | |
dc.description.status | Peer reviewed | en |
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