Ramanujan sums as supercharacters

Details Ramanujan sums as supercharacters Ramanujan sums as supercharacters

2012-01-05

arxiv.org/abs/1201.1060v3

Mathematics

Number Theory

33 pages. Comments welcome

Scientific paper

We demonstrate that many of the fundamental algebraic properties of Ramanujan
sums can be deduced using the theory of supercharacters, recently developed by
Diaconis-Isaacs and Andre. This machinery frequently yields one-line proofs of
difficult identities and provides many novel formulas. Along the way, we
develop a general theory of superclass arithmetic for arbitrary finite groups.

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