The number of unimodular zeros of self-reciprocal polynomials with coefficients in a finite set

TL;DR

This paper investigates the zeros of self-reciprocal algebraic polynomials with coefficients from a finite set, focusing on their zeros on the unit circle and real zeros of related trigonometric polynomials.

Contribution

It provides new bounds and insights into the number of zeros of self-reciprocal polynomials with coefficients in a finite set, a topic with applications in algebra and analysis.

Findings

Bounds on the number of zeros on the unit circle

Results on the number of real zeros of associated trigonometric polynomials

Characterization of zeros for polynomials with coefficients in finite sets

Abstract

We study the number of real zeros of trigonometric polynomials in a period and the number of zeros of self-reciprocal algebraic polynomials on the unit circle under the assumption that their coefficients are in a fixed finite set of real numbers.