CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Large Sieve Inequalities via Subharmonic Methods and the Mahler Measure of the Fekete Polynomials

  Published:2007-08-01
 Printed: Aug 2007
  • T. Erdélyi
  • D. S. Lubinsky
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We investigate large sieve inequalities such as \[ \frac{1}{m}\sum_{j=1}^{m}\psi ( \log | P( e^{i\tau _{j}}) | ) \leq \frac{C}{2\pi }\int_{0}^{2\pi }\psi \left( \log [ e| P( e^{i\tau }) | ] \right) \,d\tau , \] 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.
MSC Classifications: 41A17 show english descriptions Inequalities in approximation (Bernstein, Jackson, Nikol'skiii-type inequalities) 41A17 - Inequalities in approximation (Bernstein, Jackson, Nikol'skiii-type inequalities)
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/