Diophantine Equations in Many Variables
| dc.contributor.advisor | Brüdern, Jörg Prof. Dr. | |
| dc.contributor.author | Dumke, Jan Henrik | |
| dc.date.accessioned | 2014-11-06T10:50:50Z | |
| dc.date.available | 2014-11-06T10:50:50Z | |
| dc.date.issued | 2014-11-06 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-0023-992F-5 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-4773 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Diophantine Equations in Many Variables | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Brüdern, Jörg Prof. Dr. | |
| dc.date.examination | 2014-10-08 | |
| dc.description.abstracteng | Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degrees $d_1, . . . , d_r$. A contemporary version of a conjecture attributed to E. Artin states that $F_1, . . . , F_r$ have a common non-trivial zero whenever $n > d_1^2 + · · · + d_r^2$. We prove this for a single quintic form $(i.e.~ r = 1, d_1 = 5)$, provided that the cardinality of the residue class field exceeds 9. We also verify the conjecture for a system comprising a cubic and a quadratic form $(i.e.~r = 2, d_1 = 3, d_2 = 2)$, whenever the residue class field is of characteristic at least 13 and has more than 37 elements. | de |
| dc.contributor.coReferee | Blomer, Valentin Prof. Dr. | |
| dc.subject.eng | p-adic forms | de |
| dc.subject.eng | forms in many variables | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-0023-992F-5-0 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 80029887X |