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Zero Distribution of Polynomials

  • Vladimir V. Andrievskii
  • Hans-Peter Blatt
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The classical theorems of Jentzsch and Szegö concern the limiting behavior of the zeros of the partial sums of a power series. More precisely, if
are the partial sums of a power series having finite positive radius of convergence ρ, then Jentzsch [91] proved that each point of the circle of convergence C ρ := {z: |z| = ρ} is a limit point of zeros of polynomials s n (z), n = 1, 2,... . Szegö [170] substantially improved this result by showing that there is a subsequence for which the zeros of the partial sums are uniformly distributed in angle; that is, if S(α, β) is the sector
, and Z n (A) denotes the number of zeros of s n in the set A, then
(0.1)
for all sectors S(α, β).

Keywords

Maximum Principle Green Function Conformal Mapping Jordan Curve Type Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Vladimir V. Andrievskii
    • 1
  • Hans-Peter Blatt
    • 2
  1. 1.Department of Mathematics and Computer ScienceKent State UniversityKentUSA
  2. 2.Mathematisch-Geographische FakultätKatholische Universität EichstättEichstättGermany

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