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Article: An extremal property of fekete polynomials
Title  An extremal property of fekete polynomials 

Authors  
Keywords  class number +/ 1 coefficients merit factor Fekete polynomials Turyn polynomials 
Issue Date  2000 
Publisher  American Mathematical Society. 
Citation  American Mathematical Society Proceedings, 2000, v. 129 n. 1, p. 1927 How to Cite? 
Abstract  The 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 L4 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(N1) x(N1) with odd N and a(n) = +/1. If [GRAPHICS] then N must be an odd prime and f(x) is +/ Fq (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 Identifier  http://hdl.handle.net/10722/44900 
ISSN  2015 Impact Factor: 0.7 2015 SCImago Journal Rankings: 1.082 
DC Field  Value  Language 

dc.contributor.author  Borwein, P  en_HK 
dc.contributor.author  Choi, KKS  en_HK 
dc.contributor.author  Yazdani, S  en_HK 
dc.date.accessioned  20071030T06:12:59Z   
dc.date.available  20071030T06:12:59Z   
dc.date.issued  2000  en_HK 
dc.identifier.citation  American Mathematical Society Proceedings, 2000, v. 129 n. 1, p. 1927  en_HK 
dc.identifier.issn  00029939  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/44900   
dc.description.abstract  The 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 L4 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(N1) x(N1) with odd N and a(n) = +/1. If [GRAPHICS] then N must be an odd prime and f(x) is +/ Fq (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.extent  174852 bytes   
dc.format.extent  2143 bytes   
dc.format.mimetype  application/pdf   
dc.format.mimetype  text/plain   
dc.language  eng  en_HK 
dc.publisher  American Mathematical Society.  en_HK 
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.rights  First published in American Mathematical Society Proceedings, 2000, v. 129 n. 1, p. 1927, published by the American Mathematical Society,  en_HK 
dc.subject  class number  en_HK 
dc.subject  +/ 1 coefficients  en_HK 
dc.subject  merit factor  en_HK 
dc.subject  Fekete polynomials  en_HK 
dc.subject  Turyn polynomials  en_HK 
dc.title  An extremal property of fekete polynomials  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=00029939&volume=129&issue=1&spage=19&epage=27&date=2000&atitle=An+extremal+property+of+fekete+polynomials  en_HK 
dc.description.nature  published_or_final_version  en_HK 
dc.identifier.scopus  eid_2s2.033646827541   
dc.identifier.hkuros  53170   