A symmetry property of some harmonic algebraic curves

Details A symmetry property of some harmonic algebraic curves A symmetry property of some harmonic algebraic curves

2008-05-14

arxiv.org/abs/0805.2016v1

Mathematics

General Mathematics

Scientific paper

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 $\Arg(P(z))=\theta$, form a regular $n$-gon, where $n$ is the degree
of $P$.

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