| dc.contributor.advisor | Brüdern, Jörg Prof. Dr. | |
| dc.contributor.author | Kaesberg, Miriam Sophie | |
| dc.date.accessioned | 2021-02-25T13:13:17Z | |
| dc.date.available | 2021-02-25T13:13:17Z | |
| dc.date.issued | 2021-02-25 | |
| dc.identifier.uri | http://hdl.handle.net/21.11130/00-1735-0000-0005-158A-8 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-8462 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Two Cases of Artin's Conjecture | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Brüdern, Jörg Prof. Dr. | |
| dc.date.examination | 2020-12-18 | |
| dc.description.abstracteng | Let $f_1, \dots, f_R$ be forms of degree $k_1, \dots, k_R$ in $s$ variables. A generalised version of a conjecture by Artin states that the equations $f_1= \dots=f_R=0$ have a non-trivial $p$-adic solution for all primes $p$ provided that $s > k_1^2 + \dots + k_R^2$. This thesis proves Artin's conjecture for two diagonal forms of degree $k$ for odd primes $p$. Furthermore, it improves on this bound in the case of one diagonal cubic form and one linear form by showing that $s \ge 8$ variables are sufficient to ensure a non-trivial $p$-adic solution for all primes instead of the predicted $s \ge 11$ variables. | de |
| dc.contributor.coReferee | Mihailescu, Preda Prof. Dr. | |
| dc.subject.eng | $p$-adic solutions | de |
| dc.subject.eng | Artin's conjecture | de |
| dc.subject.eng | Diagonal forms | de |
| dc.subject.eng | Additive forms | de |
| dc.subject.eng | Pairs of forms | de |
| dc.subject.eng | Cubic forms | de |
| dc.subject.eng | Solutions in $\mathbb{Q}_p$ | de |
| dc.subject.eng | Analytic number theory | de |
| dc.subject.eng | Diophantine equations in many variables | de |
| dc.subject.eng | Congruences in many variables | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-21.11130/00-1735-0000-0005-158A-8-5 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematik (PPN61756535X) | de |
| dc.identifier.ppn | 1749484145 | |