In this dissertation we show that the Giulietti-Ughi arc is not complete for large primes. This arc is complete for primes which are congruent to three modulo four and less than thirty one. The cardinality of this arc has the same order as the Lunelli-Sce bound. We use two powerful theorems, one on the classifications of Galois groups of quintic polynomials and the other, the Čebotarev density theorem for function fields to show that there exist points on a certain curve which are not covered by the arc. We then outline a technique which could be used to extend the arc to a complete arc.
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/3584 |
| Date | 28 August 2008 |
| Creators | Ghosh, Rohit, 1978- |
| Contributors | Voloch, José Felipe |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | electronic |
| Rights | Copyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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