Coefficients of cyclotomic polynomials

Abstract

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 $m\ge 1$, $\{a(mn,k)|n,k\in \mathbb{N}\}=\mathbb{Z}$. In this paper, we improve this result and prove that for any integers $s>t\ge 0$, $$\{a(ns+t,k)|n,k\in \mathbb{N}\}=\mathbb{Z}.$$

arXiv comment5pages

References in corpus (2)

• Value distribution of Ramanujan sums and of cyclotomic polynomial coefficients
• Reciprocal cyclotomic polynomials