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arXiv · 1004.3550

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

Patrick S. Fleming·Stephan Ramon Garcia·Gizem Karaali
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Abstract

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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Patrick S. Fleming, Stephan Ramon Garcia, Gizem Karaali. 2010-07-02. Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs. https://arxiv.org/abs/1004.3550

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