Generalized cyclotomic polynomials associated with regular systems of divisors and arbitrary sets of positive integers

2024/05/02 by László Tóth, Tóth, László
Mathematics · #11A25 #11C08 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary: 11B83 #Secondary 11A05

paper · pdf · doi:10.48550/arxiv.2405.01278

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study the generalized cyclotomic polynomials Φ_A,S,n(x) associated with a regular system A of divisors and an arbitrary set S of positive integers. We show that all of these polynomials have integer coefficients, they can be expressed as the product of certain classical cyclotomic polynomials Φ_d(x) with d| n, and enjoy many other properties which are similar to the classical and unitary cases. We also point out some related Menon-type identities. One of them seems to be new even for the cyclotomic polynomials Φ_n(x).

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