The Graphic Nature of Gaussian Periods

Recent work has shown that the study of supercharacters on abelian groups provides a natural framework with which to study the properties of 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, this approach reveals that these classical objects display a dazzling array of visual patterns of great complexity and remarkable subtlety

Four Quotient Set Gems

Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years

An Exhibition of Exponential Sums: Visualizing Supercharacters

We discuss a simple mathematical mechanism that produces a variety of striking images of great complexity and subtlety. We briefly explain this approach and present a selection of attractive images obtained using this technique