The graphic nature of Gaussian periods

TL;DR

This paper introduces a novel perspective on Gaussian periods using supercharacters on abelian groups, revealing their complex visual patterns and deep number-theoretic properties.

Contribution

It pioneers the study of Gaussian periods through supercharacter theory, uncovering intricate visual structures and new insights into their mathematical nature.

Findings

Gaussian periods exhibit complex visual patterns

Supercharacter framework provides new understanding of exponential sums

Reveals subtle properties of classical number-theoretic objects

Abstract

Recent work has shown that the study of supercharacters on abelian groups provides a natural framework within which to study certain exponential sums of interest in number theory. Our aim here is to initiate the study of Gaussian periods from this novel perspective. Among other things, our approach reveals that these classical objects display dazzling visual patterns of great complexity and remarkable subtlety.