Advertisement

The Ramanujan Journal

, Volume 9, Issue 1–2, pp 19–23 | Cite as

Self-Inversive Polynomials with All Zeros on the Unit Circle

  • A. Schinzel
Article

Abstract

Conditions are given in the coefficients of a self-inversive polynomial under which all its zeros are on the unit circle.

Keywords

self-inversive polynomials zeros unit circle 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F.F. Bonsall and M. Marden, “Zeros of self-inversive polynomials,” Proc. Amer. Math. Soc. 3 (1952), 471–475.Google Scholar
  2. 2.
    A. Cohn, “Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise,” Math. Zeit. 14 (1922), 110–148.CrossRefGoogle Scholar
  3. 3.
    P. Lakatos, “On zeros of reciprocal polynomials,” C. R. Math. Rep. Acad. Sci. Canada 24 (2002), 91–96.zbMATHGoogle Scholar
  4. 4.
    G. Pólya and G. Szegő, Problems and Theorems in Analysis, vol. II, Springer 1976.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institute of Mathematics, Polish Academy of SciencesWarszawa 10Poland

Personalised recommendations