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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.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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