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Computational Methods and Function Theory

, Volume 9, Issue 2, pp 435–442 | Cite as

Fixed Points of Conjugated Blaschke Products with Applications to Gravitational Lensing

  • Ludwig Kuznia
  • Erik Lundberg
Article

Abstract

A conjecture in astronomy was recently resolved as an accidental corollary to a theorem regarding zeros of certain planar harmonic maps. As a step towards extending the Fundamental Theorem of Algebra, the theorem gave a bound of 5nt 5 for the number of zeros of a function of the form \(r(z) - \bar{z}\), where r(z) is rational of degree n. In this paper, we will investigate the case when r(z) is a Blaschke product. The resulting (sharp) bound is n + 3 and the proof is simple. We discuss an application to gravitational lenses consisting of collinear point masses.

Keywords

Blaschke product gravitational lens collinear point masses proper self-maps 

2000 MSC

Primary 30D05 Secondary 83C99 26C15 

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Copyright information

© Heldermann  Verlag 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA

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