Standard

On asymptotics of the uniform norm of polynomials with zeros at the roots of unity. / Makarov, B. M.; Podkorytov, A. N.

In: Analysis Mathematica, Vol. 30, No. 3, 01.12.2004, p. 223-241.

Research output: Contribution to journal › Article › peer-review

Harvard

Makarov, BM & Podkorytov, AN 2004, 'On asymptotics of the uniform norm of polynomials with zeros at the roots of unity', Analysis Mathematica, vol. 30, no. 3, pp. 223-241. https://doi.org/10.1023/B:ANAM.0000043312.46324.b7

APA

Makarov, B. M., & Podkorytov, A. N. (2004). On asymptotics of the uniform norm of polynomials with zeros at the roots of unity. Analysis Mathematica, 30(3), 223-241. https://doi.org/10.1023/B:ANAM.0000043312.46324.b7

Vancouver

Makarov BM, Podkorytov AN. On asymptotics of the uniform norm of polynomials with zeros at the roots of unity. Analysis Mathematica. 2004 Dec 1;30(3):223-241. https://doi.org/10.1023/B:ANAM.0000043312.46324.b7

Author

Makarov, B. M. ; Podkorytov, A. N. / On asymptotics of the uniform norm of polynomials with zeros at the roots of unity. In: Analysis Mathematica. 2004 ; Vol. 30, No. 3. pp. 223-241.

BibTeX

@article{953035051d894738b5b6af38ea193baf,
title = "On asymptotics of the uniform norm of polynomials with zeros at the roots of unity",
abstract = "The work is related to the problem by P. Erdo{double acute}s about the estimation of the numbers, where {pipe}zj{pipe} = 1, as N→∞. We shall deal with the case where the z j are all possible roots of the unity ordered in such a way that all the roots of degree n follow the roots of degree n-1. Within the group of roots of degree n, the enumeration can vary. We prove that ln A N grows like √N, and we get estimates of possible values of the lower limit of the ratio (ln A N/√N as well as exact bounds of the upper limit of this ratio.",
author = "Makarov, {B. M.} and Podkorytov, {A. N.}",
year = "2004",
month = dec,
day = "1",
doi = "10.1023/B:ANAM.0000043312.46324.b7",
language = "English",
volume = "30",
pages = "223--241",
journal = "Analysis Mathematica",
issn = "0133-3852",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - On asymptotics of the uniform norm of polynomials with zeros at the roots of unity

AU - Makarov, B. M.

AU - Podkorytov, A. N.

PY - 2004/12/1

Y1 - 2004/12/1

N2 - The work is related to the problem by P. Erdo{double acute}s about the estimation of the numbers, where {pipe}zj{pipe} = 1, as N→∞. We shall deal with the case where the z j are all possible roots of the unity ordered in such a way that all the roots of degree n follow the roots of degree n-1. Within the group of roots of degree n, the enumeration can vary. We prove that ln A N grows like √N, and we get estimates of possible values of the lower limit of the ratio (ln A N/√N as well as exact bounds of the upper limit of this ratio.

AB - The work is related to the problem by P. Erdo{double acute}s about the estimation of the numbers, where {pipe}zj{pipe} = 1, as N→∞. We shall deal with the case where the z j are all possible roots of the unity ordered in such a way that all the roots of degree n follow the roots of degree n-1. Within the group of roots of degree n, the enumeration can vary. We prove that ln A N grows like √N, and we get estimates of possible values of the lower limit of the ratio (ln A N/√N as well as exact bounds of the upper limit of this ratio.

UR - http://www.scopus.com/inward/record.url?scp=84867994787&partnerID=8YFLogxK

U2 - 10.1023/B:ANAM.0000043312.46324.b7

DO - 10.1023/B:ANAM.0000043312.46324.b7

M3 - Article

AN - SCOPUS:84867994787

VL - 30

SP - 223

EP - 241

JO - Analysis Mathematica

JF - Analysis Mathematica

SN - 0133-3852

IS - 3

ER -

ID: 48414308