Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online June 29, 2022

Copyright © The Korean Mathematical Society.

Some polynomials with unimodular roots

Arturas Dubickas

Vilnius University

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 $[0,2\pi)$.

Keywords: Self-reciprocal polynomials, unimodular roots, trigonometric polynomials

MSC numbers: 12D10, 26C10, 42A05

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