Coefficients of cyclotomic polynomials

By Pingzhi Yuan. 2009

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Let $a(n, k)$ be the $k$-th coefficient of the $n$-th cyclotomic polynomial. Recently, Ji, Li and Moree \cite{JLM09} proved that for any integer $m\ge1$, $\{a(mn, k)| n, k\in\mathbb{N}\}=\mathbb{Z}$. In this paper, we improve this result and prove that for any integers $s>t\ge0$, $$\{a(ns+t, k)| n, k\in\mathbb{N}\}=\mathbb{Z}.$$

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/065036834d7a8f805d51cdfba866324e139a3f0d