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arXiv · 1201.1060

Ramanujan sums as supercharacters

Christopher F. Fowler·Stephan Ramon Garcia·Gizem Karaali
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Abstract

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.

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Christopher F. Fowler, Stephan Ramon Garcia, Gizem Karaali. 2012-12-14. Ramanujan sums as supercharacters. https://arxiv.org/abs/1201.1060

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