A note on heights of cyclotomic polynomials

Bachman, Gennady; Bao, Christopher; Wu, Shenlone

doi:10.2140/involve.2025.18.363

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A note on heights of cyclotomic polynomials

Gennady Bachman, Christopher Bao and Shenlone Wu

Vol. 18 (2025), No. 2, 363–372

DOI: 10.2140/involve.2025.18.363

Abstract

We show that for any positive integer $h$ , either $h$ or $h + 1$ is a height of some cyclotomic polynomial $Φ_{n}$ , where $n$ is a product of three distinct primes.

Keywords

cyclotomic polynomials, inclusion-exclusion polynomials, heights of polynomials

Mathematical Subject Classification

Primary: 11B83, 11C08

Milestones

Received: 12 September 2023

Revised: 12 December 2023

Accepted: 13 December 2023

Published: 26 February 2025

Communicated by Ken Ono

Authors

Gennady Bachman
Department of Mathematical Sciences University of Nevada Las Vegas Las Vegas, NV United States

Christopher Bao
University of Nevada Las Vegas Las Vegas, NV United States

Shenlone Wu
University of Nevada Las Vegas Las Vegas, NV United States

Vol. 18, No. 2, 2025