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

Abstract

AbstractWe investigate large sieve inequalities such as where 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 ≤ Ƭ1 < Ƭ2 < … < Ƭm ≤ 2π. 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.