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On towers of function fields over finite fields
Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867613955200909312 |
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| access_status_str | Open Access |
| author | Lotter, Ernest Christiaan |
| author2 | Green, B. W. |
| author_browse | Green, B. W. Lotter, Ernest Christiaan |
| author_facet | Green, B. W. Lotter, Ernest Christiaan |
| author_sort | Lotter, Ernest Christiaan |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/1283 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:44:21.913Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/1283 On towers of function fields over finite fields Lotter, Ernest Christiaan Green, B. W. University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Class field towers Algebraic fields Function algebras Dissertations -- Mathematics Theses -- Mathematics Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007. Explicit towers of algebraic function fields over finite fields are studied by considering their ramification behaviour and complete splitting. While the majority of towers in the literature are recursively defined by a single defining equation in variable separated form at each step, we consider towers which may have different defining equations at each step and with arbitrary defining polynomials. The ramification and completely splitting loci are analysed by directed graphs with irreducible polynomials as vertices. Algorithms are exhibited to construct these graphs in the case of n-step and -finite towers. These techniques are applied to find new tamely ramified n-step towers for 1 n 3. Various new tame towers are found, including a family of towers of cubic extensions for which numerical evidence suggests that it is asymptotically optimal over the finite field with p2 elements for each prime p 5. Families of wildly ramified Artin-Schreier towers over small finite fields which are candidates to be asymptotically good are also considered using our method. Doctoral 2008-07-17T10:01:25Z 2010-06-01T08:17:20Z 2008-07-17T10:01:25Z 2010-06-01T08:17:20Z 2007-03 Thesis http://hdl.handle.net/10019.1/1283 en University of Stellenbosch application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Class field towers Algebraic fields Function algebras Dissertations -- Mathematics Theses -- Mathematics Lotter, Ernest Christiaan On towers of function fields over finite fields |
| title | On towers of function fields over finite fields |
| title_full | On towers of function fields over finite fields |
| title_fullStr | On towers of function fields over finite fields |
| title_full_unstemmed | On towers of function fields over finite fields |
| title_short | On towers of function fields over finite fields |
| title_sort | on towers of function fields over finite fields |
| topic | Class field towers Algebraic fields Function algebras Dissertations -- Mathematics Theses -- Mathematics |
| url | http://hdl.handle.net/10019.1/1283 |
| work_keys_str_mv | AT lotterernestchristiaan ontowersoffunctionfieldsoverfinitefields |