Ramanujan sums as supercharacters

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.

32 pages. Comments welcome

References in corpus (2)

• Ramanujan sums for signal processing of low frequency noise
• Some remarks on Ramanujan sums and cyclotomic polynomials

Cited by in corpus (2)

• Twin Primes In Quadratic Arithmetic Progressions
• Spectral Methods And Prime Numbers Counting Problems