## The location of critical points of finite Blaschke products

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- by David A. Singer PDF
- Conform. Geom. Dyn.
**10**(2006), 117-124 Request permission

## Abstract:

A theorem of Bôcher and Grace states that the critical points of a cubic polynomial are the foci of an ellipse tangent to the sides of the triangle joining the zeros. A more general result of Siebert and others states that the critical points of a polynomial of degree $N$ are the algebraic foci of a curve of class $N-1$ which is tangent to the lines joining pairs of zeroes. We prove the analogous results for hyperbolic polynomials, that is, for Blaschke products with $N$ roots in the unit disc.## References

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## Additional Information

**David A. Singer**- Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
- Email: david.singer@case.edu
- Received by editor(s): January 16, 2006
- Published electronically: June 7, 2006
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**10**(2006), 117-124 - MSC (2000): Primary 53A35; Secondary 30D50
- DOI: https://doi.org/10.1090/S1088-4173-06-00145-7
- MathSciNet review: 2223044