Samantha Platt, University of Oregon
Authors: Samantha Platt
2023 AWM Research Symposium
Poster Presentation

Gaussian periods have been studied for centuries in the realms of number theory, field theory, cryptography, and elsewhere. However, it was only within the last decade or so that they began to be studied from a visual perspective. By plotting Gaussian periods in the complex plane, many interesting and insightful patterns can be seen, leading to various conjectures and theorems about their properties. For this presentation, we offer a description of Gaussian periods, along with examples of the structure that can occur when plotting them in the complex plane. In addition to this, we offer two ways in which this study can be generalized to other situations---one relating to supercharacter theory, the other relating to class field theory---along with visual examples of each.

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