Value distribution of cyclotomic polynomial coefficients (Q2893505)

Let \(a_n(k)\) be the \(k\)th coefficient, \(k=0,\dots ,\varphi (n)\), of the \(n\)th cyclotomic polynomial \(\Phi_n(x)\), and \(c_n(k)\) the \(k\)th coefficient, \(k=0,1,\dots \), of the Maclaurin expansion of \(1/\Phi_n(x)\). In the paper explicit values for \(\lim_{n\to \infty} (1/x)\sum_{n\leq k}a_n(k)\), \(\lim_{n\to \infty} (1/x)\sum_{n\leq k}c_n(k)\), as well as for the asymptotic densities of the sets such that \(a_n(k)=v\) or \(c_n(k)=v\) are proved. The paper also contains variations on the mentioned results. A rich computational material is collected in the paper, and various open problems are formulated.