# 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 $n > d_1^2 + · · · + d_r^2$. de 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. 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
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