In our study Fq denotes the finite field with q elements. It is interesting to construct curves of given genus over Fq with many Fq -rational points. Drinfeld modular curves can be used to construct that kind of curves over Fq . In this study we will use reductions of the Drinfeld modular curves X_{0} (n) to obtain curves over finite fields with many rational points. The main idea is to divide the Drinfeld modular curves by an Atkin-Lehner involution which has many fixed points to obtain a quotient with a better #{rational points} /genus ratio. If we divide the Drinfeld modular curve X_{0} (n) by an involution W, then the number of rational points of the
quotient curve WX_{0} (n) is not less than half of the original number. On the other hand, if this involution has many fixed points, then by the Hurwitz-Genus formula the genus of the curve WX_{0} (n) is much less than half of the g (X_{0}(n)).
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12613118/index.pdf |
| Date | 01 March 2011 |
| Creators | Cam, Vural |
| Contributors | Ozbudak, Ferruh |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for METU campus |
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