Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs

Details Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs

2010-04-20

arxiv.org/abs/1004.3550v2

Revised and final version at: Journal of Number Theory 131 (2011), pp.661-680

Mathematics

Number Theory

20 pages

Scientific paper

We study the representation theory of a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of "magical" combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.

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