On the number of terms of some families of the ternary cyclotomic polynomials $\Phi_{3p_2p_3}$

TL;DR

This paper investigates the number of non-zero terms in certain ternary cyclotomic polynomials, deriving formulas by decomposing them into smaller sub-polynomials and analyzing their properties.

Contribution

It provides explicit formulas for the number of terms in specific families of ternary cyclotomic polynomials, enhancing understanding of their structure.

Findings

Formulas for the number of non-zero terms in the studied families

Decomposition of cyclotomic polynomials into sub-polynomials

Analysis of properties of these sub-polynomials

Abstract

We study the number of non-zero terms in two specific families of ternary cyclotomic polynomial, we find formulas for the number of terms by writing the cyclotomic polynomial as a sum of smaller sub-polynomials and study the properties of these polynomial.