Fixed points of conjugated Blaschke products with applications to gravitational lensing
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 an extension of the fundamental theorem of algebra, the theorem gives a bound of \(5n-5\) for the number of zeros of a function of the form \(r(z) - \bar z\), where \(r(z)\) is rational of degree \(n\). In the paper under review, the authors investigate the case when \(r(z)\) is a Blaschke product. The resulting (sharp) bound is \(n+3\), and the proof is simple. They also discuss an application to gravitational lenses consisting of collinear point masses.
scientific article; zbMATH DE number 5648467