Artins förmodan: p-adiska tal, ändliga kroppar och ekvationer utan heltalslösningar
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Typ
Examensarbete för kandidatexamen
Bachelor Thesis
Bachelor Thesis
Program
Publicerad
2019
Författare
Karlsson, Alexander
Wahl, Kajsa
Klyver, Markus
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
This paper is based on Artin's conjecture concerning homogeneous polynomial equations. The conjecture is false in general but it is still true in many cases. One of our goals is to motivate why the conjecture is formulated the way it is. Moreover, we present a counterproof to the conjecture and we prove the conjecture in one specific case. We construct the p-adic numbers as the conjecture is expressed in terms of p-adic numbers and we introduce theory on finite fields, as it is needed in the motivation of the conjecture, the counterproof and in the proof of the specific case.
Beskrivning
Ämne/nyckelord
Grundläggande vetenskaper , Matematik , Basic Sciences , Mathematics