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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Akiyama and D. Y. Kwon, Constructions of Pisot and Salem numbers with flat palindromes, Monatsh. Math., 155 (2008), 265–275.
P. Borwein, T. Erdélyi, R. Ferguson and R. Lockhart, On the zeros of cosine polynomials: Solution to a problem of Littlewood, Ann. of Math., 167 (2008), 1109–1117.
W. Chen, On the polynomials with all their zeros on the unit circle, J. Math. Anal. Appl., 190 (1995), 714–724.
A. Cohn, Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z., 14 (1922), 110–148.
J. L. Coolidge, The continuity of the roots of an algebraic equation, Ann. of Math., 9 (1908), 116–118.
D. Y. Kwon, Reciprocal polynomials with all zeros on the unit circle, Acta Math. Hungar., 131 (2011), 285–294.
P. Lakatos, A new construction of Salem polynomials, C.R. Math. Acad. Sci. Soc. R. Can., 25 (2003), 47–54.
P. Lakatos and L. Losonczi, Circular interlacing with reciprocal polynomials, Math. Inequal. Appl., 10 (2007), 761–769.
J. E. Littlewood, Some Problems in Real and Complex Analysis, Heath Mathematical Monographs, D. C. Heath and Co. (Lexington, Mass., 1968).
J. McKee and C. Smyth, There are Salem numbers of every trace, Bull. London Math. Soc., 37 (2005), 25–36.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kwon, D. Reciprocal polynomials with all but two zeros on the unit circle. Acta Math Hung 134, 472–480 (2012). https://doi.org/10.1007/s10474-011-0176-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-011-0176-1