On a certain family of inverse ternary cyclotomic polynomials

TL;DR

This paper investigates a specific family of inverse ternary cyclotomic polynomials, deriving formulas for their height and identifying conditions under which they are flat, contributing to the understanding of their algebraic properties.

Contribution

It provides a formula for the height of inverse ternary cyclotomic polynomials and characterizes all flat polynomials within this family.

Findings

Derived a formula for the height of the polynomials

Characterized all flat polynomials in the family

Enhanced understanding of algebraic properties of inverse ternary cyclotomic polynomials

Abstract

We study a family of inverse ternary cyclotomic polynomials $\Psi_{pqr}$ in which $r\le\varphi(pq)$ is a positive linear combination of $p$ and $q$. We derive a formula for the height of such polynomial and characterize all flat polynomials in this family.