Ramanujan sums as supercharacters |
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Authors: | Christopher F Fowler Stephan Ramon Garcia Gizem Karaali |
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Institution: | 1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA 2. Department of Mathematics, Pomona College, Claremont, CA, 91711, USA
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Abstract: | 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. |
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