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.Net visualization suite for Kloosterman cardioid research
Root, WilliamEckberg, CarlGrone, Robert
ix, 48 p. : ill.
In August 2007 a parallel/distributed computer program designed and coded by a team of SDSU computer science graduate students, after running continuously for more than seven months on a 45-node commodity PC cluster, emitted a single 5-digit integer: a prime number counterexample disproving the Evans Conjecture on Kloosterman Sums. In the course of their research, the students discovered another fascinating fact: when the points on the unit circle corresponding to the set of all normalized Kloosterman sums for a given prime p were computed in a particular order and connected by line segments, the resulting graph contained a pronounced embedded epicycloidal locus. In particular, it appeared that for primes p for which the finite field GF(p) has g=2 as a generator, the locus is a cardioid whose axis of symmetry differs for different p . This thesis project is one of a group of four related thesis projects aimed at developing a suite of software tools to collect, organize, and visualize empirical data about these "Kloosterman cardioids" to aid in the search for a rigorous mathematical explanation for their existence. In particular, this thesis project developed .NET software for visualization of Kloosterman cardioids, including methods for enhancing the cardioidal locus image for those values of p sufficiently large that the locus would otherwise be obscured due to the density of the O (p_) segments in the Kloosterman sum graph not contributing to the locus
Includes bibliographical references (p. 27)
Master of Science (M.S.) San Diego State University, 2012
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