The Quintic Gauss Sums

Fossi, Talom Leopold

dc.contributor.advisor	Patterson, Samuel James Prof. Dr.	de
dc.contributor.author	Fossi, Talom Leopold	de
dc.date.accessioned	2004-09-14T15:27:25Z	de
dc.date.accessioned	2013-01-18T13:20:25Z	de
dc.date.available	2013-01-30T23:51:28Z	de
dc.date.issued	2004-09-14	de
dc.identifier.uri	http://hdl.handle.net/11858/00-1735-0000-0006-B3BD-8	de
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-2471
dc.description.abstract	Eine moeglische Veralgeneinerung von Casselscher Formel ist in der Fassung nicht moglich. Wir konstruiiren fundamentale Bereiche zyklotomischer Koerper und dessen kombinatorischen Geometrie. Die Eulersche relation is erfuelt. wir zeigen, wie man am besten eine kanonische Einheitswuerzel herausfinden kann. Einige Vermutungen ueber die Gaussschen summen mit solchen kononischen Einheitswuerzel, nach unseren numerische Ausgabe, sind gegeben. Wir haben an Anhang noch einn Beweise ueber die gaussschen Summen die rational sind gegeben.	de
dc.format.mimetype	application/pdf	de
dc.language.iso	eng	de
dc.rights.uri	http://webdoc.sub.gwdg.de/diss/copyr_diss.html	de
dc.title	The Quintic Gauss Sums	de
dc.type	doctoralThesis	de
dc.title.translated	Die Gaussschen Summen von Ordnung fuenf	de
dc.contributor.referee	Stuhler, Ulrich Prof. Dr.	de
dc.date.examination	2002-10-25	de
dc.subject.dnb	510 Mathematik	de
dc.description.abstracteng	We investigate the possibility of generalization of the Cassel-McGettrick formula for the quintic Gauss sums. We construct a fundamental region for the fifth cyclotomic field. we describe in general the combinatoric of their geometry. The formula obtained so far satisfied a recurrence relation. The Euler relation is proved. We show how to extract canonicaly a root of unity once we have contructed the fundamental region. The numerical computation shows that a generalization of Cassels-McGettrick formula fails. One should actually attempt to modify the shape of the fundamental region to see if there is a new formula. We prove that there are new conjectures involving Gauss sums. This is actually supported by strong computation within a certain range. In the appendix we show that, there are Gauss sums which are rational intgers. we explicitely give a proof and how to find them.	de
dc.contributor.coReferee	Kersten, Ina Prof. Dr.	de
dc.contributor.thirdReferee	Hartje, Kriete PD	de
dc.subject.topic	Mathematics and Computer Science	de
dc.subject.ger	Zyklotomische Koerper	de
dc.subject.ger	Cassels conjecture	de
dc.subject.ger	Gausssche Summen	de
dc.subject.ger	Jacobische Summen	de
dc.subject.ger	residue symbol	de
dc.subject.eng	cyclotomic fields	de
dc.subject.eng	cassels conjecture	de
dc.subject.eng	Gauss sums	de
dc.subject.eng	Jacobi sums	de
dc.subject.eng	character sums	de
dc.subject.eng	residue symbol	de
dc.subject.eng	fundamental region	de
dc.subject.bk	31.14 Zahlentheorie	de
dc.identifier.urn	urn:nbn:de:gbv:7-webdoc-210-2	de
dc.identifier.purl	webdoc-210	de
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	31.14 Zahlentheorie	de
dc.identifier.ppn	478434308	de

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