Periodica Mathematica Hungarica

, Volume 25, Issue 2, pp 179–190 | Cite as

Sequences of polynomials whose zeros lie on fixed lemniscates

  • K. Dilcher
  • K. B. Stolarsky
Article

Abstract

For fixed integersk≥2 we study sequences of polynomialsP n (z) with the following properties: (i) degP n → ∞; (ii) the zeros of all theP n (z) lie on a certain lemniscate withk1k foci, one of which is the origin; (iii) theP n (z) can be cut in such a way that the zeros of the “lower part” all lie on the unit circle and those of the “upper part” lie on a lemniscate having the foci in (ii) excluding the origin. Several special cases and examples are considered.

Mathematics subject classification numbers, 1991

Primary 30-XX 

Key words and phrases

Sequences of polinomials lemniscate 

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Copyright information

© Akadémiai Kiadó 1992

Authors and Affiliations

  • K. Dilcher
    • 1
  • K. B. Stolarsky
    • 2
  1. 1.Department of Mathematics Statistics and Computing ScienceDalhousie UniversityHalifaxCanada
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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