Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs
Number Theory
2011-04-19 v2 Combinatorics
Representation Theory
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.
Cite
@article{arxiv.1004.3550,
title = {Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs},
author = {Patrick S. Fleming and Stephan Ramon Garcia and Gizem Karaali},
journal= {arXiv preprint arXiv:1004.3550},
year = {2011}
}
Comments
20 pages