Visual Aspects of Gaussian Periods and Analogues

dc.contributor.advisorEischen, Ellen
dc.contributor.authorPlatt, Samantha
dc.date.accessioned2024-08-07T21:28:29Z
dc.date.available2024-08-07T21:28:29Z
dc.date.issued2024-08-07
dc.description.abstractIn 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_US
dc.identifier.urihttps://hdl.handle.net/1794/29735
dc.language.isoen_US
dc.publisherUniversity of Oregon
dc.rightsAll Rights Reserved.
dc.subjectClass field theoryen_US
dc.subjectComplex multiplicationen_US
dc.subjectElliptic curvesen_US
dc.subjectExponential sumsen_US
dc.subjectGaussian Periodsen_US
dc.subjectSupercharacter theoryen_US
dc.titleVisual Aspects of Gaussian Periods and Analogues
dc.typeElectronic Thesis or Dissertation
thesis.degree.disciplineDepartment of Mathematics
thesis.degree.grantorUniversity of Oregon
thesis.degree.leveldoctoral
thesis.degree.namePh.D.

Files

Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Platt_oregon_0171A_13833.pdf
Size:
58.82 MB
Format:
Adobe Portable Document Format