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Article: An extremal property of fekete polynomials

TitleAn extremal property of fekete polynomials
Authors
Keywordsclass number
+/- 1 coefficients
merit factor
Fekete polynomials
Turyn polynomials
Issue Date2000
PublisherAmerican Mathematical Society.
Citation
American Mathematical Society Proceedings, 2000, v. 129 n. 1, p. 19-27 How to Cite?
AbstractThe Fekete polynomials are defined as [GRAPHICS] where (./q) is the Legendre symbol. These polynomials arise in a number of contexts in analysis and number theory. For example, after cyclic permutation they provide sequences with smallest known L-4 norm out of the polynomials with +/-1 coefficients. The main purpose of this paper is to prove the following extremal property that characterizes the Fekete polynomials by their size at roots of unity. Theorem 0.1. Let f(x) = a(1)x + a(2)x (2) + ... + a(N-1) x(N-1) with odd N and a(n) = +/-1. If [GRAPHICS] then N must be an odd prime and f(x) is +/- F-q (x). Here w:= e 2 pi i/N. This result also gives a partial answer to a problem of Harvey Cohn on character sums.
Persistent Identifierhttp://hdl.handle.net/10722/44900
ISSN
2015 Impact Factor: 0.7
2015 SCImago Journal Rankings: 1.082

 

DC FieldValueLanguage
dc.contributor.authorBorwein, Pen_HK
dc.contributor.authorChoi, KKSen_HK
dc.contributor.authorYazdani, Sen_HK
dc.date.accessioned2007-10-30T06:12:59Z-
dc.date.available2007-10-30T06:12:59Z-
dc.date.issued2000en_HK
dc.identifier.citationAmerican Mathematical Society Proceedings, 2000, v. 129 n. 1, p. 19-27en_HK
dc.identifier.issn0002-9939en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44900-
dc.description.abstractThe Fekete polynomials are defined as [GRAPHICS] where (./q) is the Legendre symbol. These polynomials arise in a number of contexts in analysis and number theory. For example, after cyclic permutation they provide sequences with smallest known L-4 norm out of the polynomials with +/-1 coefficients. The main purpose of this paper is to prove the following extremal property that characterizes the Fekete polynomials by their size at roots of unity. Theorem 0.1. Let f(x) = a(1)x + a(2)x (2) + ... + a(N-1) x(N-1) with odd N and a(n) = +/-1. If [GRAPHICS] then N must be an odd prime and f(x) is +/- F-q (x). Here w:= e 2 pi i/N. This result also gives a partial answer to a problem of Harvey Cohn on character sums.en_HK
dc.format.extent174852 bytes-
dc.format.extent2143 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherAmerican Mathematical Society.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsFirst published in American Mathematical Society Proceedings, 2000, v. 129 n. 1, p. 19-27, published by the American Mathematical Society,en_HK
dc.subjectclass numberen_HK
dc.subject+/- 1 coefficientsen_HK
dc.subjectmerit factoren_HK
dc.subjectFekete polynomialsen_HK
dc.subjectTuryn polynomialsen_HK
dc.titleAn extremal property of fekete polynomialsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0002-9939&volume=129&issue=1&spage=19&epage=27&date=2000&atitle=An+extremal+property+of+fekete+polynomialsen_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-33646827541-
dc.identifier.hkuros53170-

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