Document Type

Article - preprint

Department

Mathematics (Pomona)

Publication Date

2011

Keywords

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

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.

Comments

Pre-print from http://arxiv.org/abs/1004.3550

Final publication can be found at:

Fleming, P., Garcia, S.R., Karaali, G., Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs, J. Number Theory 131 (2011), no. 4, 661–680. MR2753270 (2012a:11114)

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© 2010 Elsevier B.V.

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