Graduation Year
Spring 2014
Document Type
Campus Only Senior Thesis
Department
Mathematics
Reader 1
Stephan Garcia
Reader 2
Winston Ou
Terms of Use & License Information
Rights Information
© 2014 Madeleine C. Bulkow
Abstract
In this thesis, we briefly review facts of representation and character theory in order to define supercharacter theories, which give a generalization of the characters on a given group. Supercharacter theories for the groups (Z/nZ)^2 and (Z/nZ)^m are constructed which contain respectively the Kloosterman sums and the Hyper-Kloosterman sums, their higher- dimensional analogue. The graphical properties of Hyper-Kloosterman sums are examined, and a conjecture made regarding a hypocycloid bound for the degree 2 Hyper-Kloosterman sums. Additionally, the orthogonality relations from a supercharacter table producing Hyper-Kloosterman sums are used to give a proof of Mordell’s bound, a previously known bound of Hyper-Kloosterman sums.
Recommended Citation
Bulkow, Madeleine C., "Hyper-Kloosterman Sums in Supercharacter Theories" (2014). Scripps Senior Theses. 361.
https://scholarship.claremont.edu/scripps_theses/361
This thesis is restricted to the Claremont Colleges current faculty, students, and staff.
