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arXiv · 0805.2016

A symmetry property of some harmonic algebraic curves

Jean-Christophe Aval·Jean-François Marckert
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Abstract

The aim of this note is to give a surprising symmetry property of some harmonic algebraic curves: when all the roots $z_i$ of a complex polynomial $P$ lie on the unit circle $\U$, the points of $\U$ different from the $z_i$, and such that $\Arg(P(z))=θ$, form a regular $n$-gon, where $n$ is the degree of $P$.

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Jean-Christophe Aval, Jean-François Marckert. 2008-05-14. A symmetry property of some harmonic algebraic curves. https://arxiv.org/abs/0805.2016

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