A new lower bound for the maximal valence of harmonic polynomials

DOI10.1007/s40315-016-0175-xzbMath1362.30005OpenAlexW2503658212MaRDI QIDQ523626

Seung-Yeop Lee, Andres Saez

Publication date: 21 April 2017

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-016-0175-x

zbMATH Keywords

harmonic polynomiallarge-degree asymptoticsvalence

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials and rational functions of one complex variable (30C10)

Related Items (5)

About the cover: visualization of harmonic functions ⋮ The valence of harmonic polynomials viewed through the probabilistic lens ⋮ On the numbers of images of two stochastic gravitational lensing models ⋮ Zeros of harmonic polynomials, critical lemniscates, and caustics ⋮ Location of the zeros of harmonic trinomials

Cites Work

• Problems and conjectures in planar harmonic mappings
• Zeros of harmonic polynomials, critical lemniscates, and caustics
• On Crofoot-Sarason's conjecture for harmonic polynomials
• The exact bound on the number of zeros of harmonic polynomials
• Counting Zeros of Harmonic Rational Functions and its Application to Gravitational Lensing
• Remarks on Wilmshurst's theorem
• The valence of harmonic polynomials
• On the number of zeros of certain harmonic polynomials
• Experiments on the Zeros of Harmonic Polynomials Using Certified Counting
• Sharp bounds for the valence of certain harmonic polynomials
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