In this paper we determine when there exists a matrix M in PGL2(F), and its form, such that L_k = D^M_k where D^M_k is a higher-order Dickson polynomial. We first examine the cases where M has projective orders 3, 4, and 6. For the order 3 case, we find that M has entries in, at worst, a quadratic extension of F. This is also true for the orders 4 and 6, but requires a restriction on the coefficients of h(x), the characteristic polynomial of L. In all cases, an explicit formula for M is given, and in the order 4 case the meaning of the extension is interpreted in terms of the Galois group of h. Lastly, we examine the case where F is finite, and offer a formula for M of order 5.
| Identifer | oai:union.ndltd.org:siu.edu/oai:opensiuc.lib.siu.edu:dissertations-1773 |
| Date | 01 December 2013 |
| Creators | Boone, Joshua Daniel |
| Publisher | OpenSIUC |
| Source Sets | Southern Illinois University Carbondale |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Dissertations |
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