Eischen, EllenPlatt, Samantha2024-08-072024-08-072024-08-07https://hdl.handle.net/1794/29735In this dissertation, we study Gaussian periods and their analogues from a visual perspective. Building on the work of Duke, Garcia, Hyde, Lutz, and others [BBF+14, BBGG+13, DGL15, GHL15], we introduce a more dynamical study of Gaussian periods, and we prove an explicit bound on the value of Gaussian periods using this framework. Additionally, we generalize the construction of Gaussian periods using the perspective of supercharacter theory. Using this new construction, we prove a result which greatly generalizes the main theorem of [DGL15]. We also initiate the visual study of Gaussian periods from the perspective of number theory and class field theory, and we define a generalized construction of Gaussian periods using this perspective. We discuss this class field theory analogue in depth when the base field is quadratic imaginary. The work presented here includes and expands upon a paper by this author [Pla24], which is set to appear in the "International Journal of Number Theory."en-USAll Rights Reserved.Class field theoryComplex multiplicationElliptic curvesExponential sumsGaussian PeriodsSupercharacter theoryElectronic Thesis or Dissertation