Products of cyclotomic polynomials on unit circle

TL;DR

This paper introduces a method to analyze the values of certain polynomials on the unit circle, leading to improved bounds on coefficients of cyclotomic and related polynomials.

Contribution

It develops a novel approach for evaluating polynomial values on the unit circle, enhancing existing bounds on cyclotomic polynomial coefficients.

Findings

Improved bounds on cyclotomic polynomial coefficients

A new method for analyzing polynomial values on the unit circle

Enhanced understanding of polynomial behavior on complex roots of unity

Abstract

We present a method to deal with the values of polynomials of type $P(z)=\prod_{d\in D}(1-z^d)^{j_d}$ on the unit circle. We use it to improve the known bounds on various measures of coefficients of cyclotomic and similar polynomials.