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arXiv · 1911.01749

Coefficients of (inverse) unitary cyclotomic polynomials

G. Jones·P. I. Kester·L. Martirosyan·P. Moree·L. Tóth·B. B. White·B. Zhang
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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 $n\ge 1$. 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.

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G. Jones, P. I. Kester, L. Martirosyan, P. Moree, L. Tóth, B. B. White, B. Zhang. 2019-11-05. Coefficients of (inverse) unitary cyclotomic polynomials. https://arxiv.org/abs/1911.01749

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