Bulletin of the Korean Mathematical Society (대한수학회보)

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SOME POLYNOMIALS WITH UNIMODULAR ROOTS

  • Dubickas, Arturas (Institute of Mathematics Faculty of Mathematics and Informatics Vilnius University)
  • Received : 2021.10.01
  • Accepted : 2022.02.23
  • Published : 2022.09.30
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Abstract

In this paper we consider a sequence of polynomials defined by some recurrence relation. They include, for instance, Poupard polynomials and Kreweras polynomials whose coefficients have some combinatorial interpretation and have been investigated before. Extending a recent result of Chapoton and Han we show that each polynomial of this sequence is a self-reciprocal polynomial with positive coefficients whose all roots are unimodular. Moreover, we prove that their arguments are uniformly distributed in the interval [0, 2𝜋).

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References

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