On the symmetry of finite sums of exponentials

Florian Pausinger; Dimitris Vartziotis

doi:10.4171/EM/446

On the symmetry of finite sums of exponentials

Florian Pausinger, Dimitris Vartziotis

School of Mathematics and Physics

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Abstract

In this note we are interested in the rich geometry of the graph of a curve γa,b : [0, 1] → C defined as γa,b(t) = exp(2πiat) + exp(2πibt), in which a, b are two different positive integers. It turns out that the sum of only two exponentials gives already rise to intriguing graphs. We determine the symmetry group and the points of self intersection of any such graph using only elementary arguments and describe various interesting phenomena that arise in the study of graphs of sums of more than two exponentials.

Original language	English
Pages (from-to)	62-73
Journal	Elemente der Mathematik
Volume	76
Issue number	2
DOIs	https://doi.org/10.4171/EM/446
Publication status	Published - 06 Apr 2021

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On the symmetry of finite sums of exponentials
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Cite this

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On the symmetry of finite sums of exponentials

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