Visual patterns in Gaussian periods

Paper Title:

Visual Aspects of Gaussian Periods and Analogues

Published on:

9 August 2023

Primary Category:

Number Theory

Paper Authors:

Samantha Platt

Bullets

Key Details

•

Gaussian periods exhibit striking visual patterns like hypocycloids when plotted in complex plane.

•

These patterns can be explained using cyclotomic polynomials and ideas from supercharacter theory.

•

Generalizations to other groups and number fields show analogous visual patterns.

•

The distribution and growth of these plots can be characterized using techniques from analytic number theory.

•

Many open questions remain about describing and explaining the intricate symmetries of these visual patterns.

Explore the topics in this paper

algebraic structures

complex plane

gaussian periods

symmetries

visual patterns

AI generated summary

Visual patterns in Gaussian periods

This paper explores visual patterns that emerge when plotting Gaussian periods in the complex plane. It summarizes key findings about symmetries and distribution of these plots. The paper also discusses generalizations to other algebraic structures beyond cyclotomic fields.