Phase Plots of Complex Functions: a Journey in Illustration

2010/07/14 by Elías Wegert, Elias Wegert, Wegert, Elias · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Analytic and geometric function theory #math.CV #msc:30A99 #msc:30D30

paper · pdf · doi:10.48550/arxiv.1007.2295

17 pages, 25 figures, to appear in Notices of the AMS

arxiv created 2010/07/14 · arxiv updated 2010/07/15

Abstract

We propose to visualize complex (meromorphic) functions f by their phase P_f:=f/|f|. Color--coding the points on the unit circle converts the function P_f to an image (the phase plot of f), which represents the function directly on its domain. We discuss how special properties of f are reflected by their phase plots and indicate several applications. In particular we reformulate a universality theorem for Riemann's Zeta function in the language of phase plots.

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