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Full-Text Articles in Number Theory
Ramanujan Sums As Supercharacters, Christopher F. Fowler '12, Stephan Ramon Garcia, Gizem Karaali
Ramanujan Sums As Supercharacters, Christopher F. Fowler '12, Stephan Ramon Garcia, Gizem Karaali
Pomona Faculty Publications and Research
The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality.