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
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