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  • 1 Department of Mathematics, Chonnam National University, Gwangju 500–757, Republic of Korea
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Abstract

We derive sufficient conditions under which all but two zeros of reciprocal polynomials lie on the unit circle, and specify the location of the remaining two zeros.

  • [1] Akiyama, S. Kwon, D. Y. 2008 Constructions of Pisot and Salem numbers with flat palindromes Monatsh. Math. 155 265275 .

  • [2] Borwein, P. Erdélyi, T. Ferguson, R. Lockhart, R. 2008 On the zeros of cosine polynomials: Solution to a problem of Littlewood Ann. of Math. 167 11091117 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [3] Chen, W. 1995 On the polynomials with all their zeros on the unit circle J. Math. Anal. Appl. 190 714724 .

  • [4] Cohn, A. 1922 Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise Math. Z. 14 110148 .

  • [5] Coolidge, J. L. 1908 The continuity of the roots of an algebraic equation Ann. of Math. 9 116118 .

  • [6] Kwon, D. Y. 2011 Reciprocal polynomials with all zeros on the unit circle Acta Math. Hungar. 131 285294 .

  • [7] Lakatos, P. 2003 A new construction of Salem polynomials C.R. Math. Acad. Sci. Soc. R. Can. 25 4754.

  • [8] Lakatos, P. Losonczi, L. 2007 Circular interlacing with reciprocal polynomials Math. Inequal. Appl. 10 761769.

  • [9] Littlewood, J. E. 1968 Some Problems in Real and Complex Analysis D. C. Heath and Co. Lexington, Mass. Heath Mathematical Monographs.

    • Search Google Scholar
    • Export Citation
  • [10] McKee, J. Smyth, C. 2005 There are Salem numbers of every trace Bull. London Math. Soc. 37 2536 .

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)