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Full-Text Articles in Physical Sciences and Mathematics
Classical Kloosterman Sums: Representation Theory, Magic Squares, And Ramanujan Multigraphs, Patrick S. Fleming, Stephan Ramon Garcia, Gizem Karaali
Classical Kloosterman Sums: Representation Theory, Magic Squares, And Ramanujan Multigraphs, Patrick S. Fleming, Stephan Ramon Garcia, Gizem Karaali
Pomona Faculty Publications and Research
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.