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June 2020 Coefficients of (inverse) unitary cyclotomic polynomials
G. Jones, P. I. Kester, L. Martirosyan, P. Moree, L. Tóth, B. B. White, B. Zhang
Kodai Math. J. 43(2): 325-338 (June 2020). DOI: 10.2996/kmj/1594313556

Abstract

The notion of block divisibility naturally leads one to introduce unitary cyclotomic polynomials $\Phi_n^*(x)$. They can be written as certain products of cyclotomic poynomials. We study the case where $n$ has two or three distinct prime factors using numerical semigroups, respectively Bachman's inclusion-exclusion polynomials. Given $m \ge 1$ we show that every integer occurs as a coefficient of $\Phi^*_{mn}(x)$ for some $n\ge 1$ following Ji, Li and Moree [9]. Here $n$ will typically have many different prime factors. We also consider similar questions for the polynomials $(x^n-1)/\Phi_n^*(x)$, the inverse unitary cyclotomic polynomials.

Citation

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G. Jones. P. I. Kester. L. Martirosyan. P. Moree. L. Tóth. B. B. White. B. Zhang. "Coefficients of (inverse) unitary cyclotomic polynomials." Kodai Math. J. 43 (2) 325 - 338, June 2020. https://doi.org/10.2996/kmj/1594313556

Information

Published: June 2020
First available in Project Euclid: 9 July 2020

zbMATH: 07227752
MathSciNet: MR4121365
Digital Object Identifier: 10.2996/kmj/1594313556

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 2 • June 2020
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