Large Sieve Inequalities via Subharmonic Methods and the Mahler Measure of the Fekete Polynomials
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We investigate large sieve inequalities such as 1/m Σ j=1m ψ(log|P(eiτ j)|) ≤ C/2π ∫02π ψ log[e|P(eiτ)|] dτ, where ψ 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 ≤ τ1 < τ2 < ⋯ < τm ≤ 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. © Canadian Mathematical Society 2007.
author list (cited authors)
Erdélyi, T., & Lubinsky, D. S.