Bounding the number of rational places using Weierstrass semigroups
| dc.creator | Geil, Olav | |
| dc.creator | Matsumoto, Ryutaroh | |
| dc.date | 2007-10-25 | |
| dc.date.accessioned | 2026-07-07T12:51:02Z | |
| dc.date.available | 2026-07-07T12:51:02Z | |
| dc.description | Let Lambda be a numerical semigroup. Assume there exists an algebraic function field over GF(q) in one variable which possesses a rational place that has Lambda as its Weierstrass semigroup. We ask the question as to how many rational places such a function field can possibly have and we derive an upper bound in terms of the generators of Lambda and q. Our bound is an improvement to a bound by Lewittes which takes into account only the multiplicity of Lambda and q. From the new bound we derive significant improvements to Serre's upper bound in the cases q=2, 3 and 4. We finally show that Lewittes' bound has important implications to the theory of towers of function fields. | |
| dc.description | 16 pages, 3 tables | |
| dc.identifier | https://arxiv.org/abs/0710.4662 | |
| dc.identifier | http://arxiv.org/abs/0710.4662 | |
| dc.identifier | Journal of Pure and Applied Algebra 213 (2009), no. 6, 1152-1156 | |
| dc.identifier | doi:10.1016/j.jpaa.2008.11.013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222866 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G15 (Primary); 11G20, 14H05, 14H25 (Secondary) | |
| dc.title | Bounding the number of rational places using Weierstrass semigroups | |
| dc.type | text |