On the number of zeros of certain harmonic polynomials

By Dmitry Khavinson, G. Swiatek. 2002

84 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/75c69421f41e7bdaa6f8aa3199c6734a3cae5ab1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Lei Tan
2. G. Cui
3. Lukas Geyer

In Geometry and Topology

1. Lei Tan
2. G. Cui
3. Lukas Geyer

Citations in the corpus

• A characterization of hyperbolic rational maps (2011, methodology): “Khavinson and Swiatek ([22]) proved that harmonic polynomials z − p(z) ,w herep is a holomorphic polynomial of degree n> 1, have at most 3n − 2 roots, and the bound is sharp for n = 2, 3. Bshouty and Lyzzaik ([ 5 ]) extended the sharpness of the bound to the cases n = 4, 5, 6 and 8, using purely alg”
• Sharp bounds for the valence of certain harmonic polynomials (2005, background): “In Khavinson and Świa̧tek (2002) it was proved that harmonic polynomials z − p(z), where p is a holomorphic polynomial of degree n > 1, have at most 3n−2 complex zeros.”