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

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Abstract

We consider 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. © 2010 Elsevier Inc.

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Fleming, P. S., Garcia, S. R., & Karaali, G. (2011). Classical Kloosterman sums: Representation theory, magic squares, and Ramanujan multigraphs. Journal of Number Theory, 131(4), 661–680. https://doi.org/10.1016/j.jnt.2010.10.009

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