Ramanujan sums as supercharacters

By Christopher F. Fowler, Stephan Ramon Garcia, Gizem Karaali. 2012

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The theory of supercharacters, recently developed by Diaconis-Isaacs and André, is 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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/566c5a0c307803944a26cea757dcad4b1f84a553