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Diophantine Equations in Many Variables

dc.contributor.advisorBrüdern, Jörg Prof. Dr.
dc.contributor.authorDumke, Jan Henrik
dc.date.accessioned2014-11-06T10:50:50Z
dc.date.available2014-11-06T10:50:50Z
dc.date.issued2014-11-06
dc.identifier.urihttp://hdl.handle.net/11858/00-1735-0000-0023-992F-5
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-4773
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject.ddc510de
dc.titleDiophantine Equations in Many Variablesde
dc.typedoctoralThesisde
dc.contributor.refereeBrüdern, Jörg Prof. Dr.
dc.date.examination2014-10-08
dc.description.abstractengLet 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.coRefereeBlomer, Valentin Prof. Dr.
dc.subject.engp-adic formsde
dc.subject.engforms in many variablesde
dc.identifier.urnurn:nbn:de:gbv:7-11858/00-1735-0000-0023-992F-5-0
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn80029887X


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