Computational Methods and Function Theory 9 (2009), No. 2, 435--442
Copyright Heldermann Verlag 2009
Ludwig Kuznia
lkuznia@mail.usf.edu , University of South Florida, Department of Mathematics and Statistics, 4204 E. Fowler Ave., PHY114, Tampa, FL 33620, U.S.A.
Erik Lundberg
elundber@mail.usf.edu , University of South Florida, Department of Mathematics and Statistics, 4204 E. Fowler Ave., PHY114, Tampa, FL 33620, U.S.A.
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 5n-5 for the number of zeros of a function of the form r(z) - 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.
MSC 2000: Primary 30D05; Secondary 83C99, 26C15.
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