Erdélyi, T.; Lubinsky, D. S. Large sieve inequalities via subharmonic methods and the Mahler measure of the Fekete polynomials. (English) Zbl 1166.41004 Can. J. Math. 59, No. 4, 730-741 (2007). Summary: We investigate large sieve inequalities such as\[ \frac{1}{m} \sum_{j=1}^m \psi(\log|P(e^{i \tau_j})|) \leq \frac{C}{2 \pi} \int_0^{2 \pi} \psi(\log[e|P(e^{i \tau})|])\,d \tau, \]where \(\psi\) is convex and increasing, \(P\) is a polynomial or an exponential of a potential, and the constant \(C\) depends on the degree of \(P\), and the distribution of the points \(0 \leq \tau_1 < \tau_2 < \dots < \tau_m \leq 2 \pi\). The method allows greater generality and is in some ways simpler than earlier ones. We apply our results to estimate the Mahler measure of Fekete polynomials. Cited in 1 ReviewCited in 11 Documents MSC: 11C08 Polynomials in number theory 11N35 Sieves 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) PDFBibTeX XMLCite \textit{T. Erdélyi} and \textit{D. S. Lubinsky}, Can. J. Math. 59, No. 4, 730--741 (2007; Zbl 1166.41004) Full Text: DOI