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

  • Fleming P
  • Garcia S
  • Karaali G
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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.

Author-supplied keywords

  • Eigenvalues
  • Kloosterman sum
  • Magic square
  • Multigraph
  • Panmagic square
  • Ramanujan graph
  • Ramanujan multigraph
  • Representation
  • Weil bound

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Authors

  • Patrick S. Fleming

  • Stephan Ramon Garcia

  • Gizem Karaali

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