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dc.contributor.advisorBüyükboduk, Kazım
dc.contributor.authorKiliçer, Pinar
dc.date.accessioned2020-12-08T07:57:57Z
dc.date.available2020-12-08T07:57:57Z
dc.date.submitted2011
dc.date.issued2018-08-06
dc.identifier.urihttps://acikbilim.yok.gov.tr/handle/20.500.12812/169646
dc.description.abstractBu çalışmada, ilk önce Stark regulatörlerini tanımlayarak, Stark varsayımını gösteriyoruz. Daha sonra, bu varsayımın değişmeli L-fonksiyonlarının s=0 da tek sıfırlı olduuğu durumlar için verilmiş varsayımını gösteriyoruz ve bu varsayımın özel bir durum içiin Hilbert'in 12. problemine çözüm sunduğunu gösteriyoruz. En son kısım da ise Rubin'in bu varsayımı genişlettiği durumu inceliyoruz.
dc.description.abstractIn this study, we state the principal Stark conjecture by defining Stark regulator which is an analogue of the regulator appearing in the Dirichlet Class Number Formula. The conjecture is independent of a choice of a set of places and a certain isomorphism of Q[G]-modules. We state Stark's refinement of this conjecture (`over Z') for abelian L-functions with simple zeros at s=0. This refinement predicts the existence of Stark units and we explain that the field generated over a totally real field k by the Stark units provides an answer to Hilbert's twelfth problem. We also express John Tate's reformulation for this refinement. Then, we give proofs of the conjecture in some simple cases and Stark's computational verification of the conjecture in a specific case. In the last chapter, we state the Rubin-Stark conjecture which is an extension of this conjecture which includes the case of abelian L-functions with higher order zeros at s=0. We end by giving proofs of the conjecture in some cases and showing its relations between the Stark conjecture.en_US
dc.languageEnglish
dc.language.isoen
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightsAttribution 4.0 United Statestr_TR
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectMatematiktr_TR
dc.subjectMathematicsen_US
dc.titleStark`s conjectures and hilbert`s twelfth problem
dc.title.alternativeStark'ın sanıları ve Hilbert'ın onikinci problemi
dc.typemasterThesis
dc.date.updated2018-08-06
dc.contributor.departmentMatematik Anabilim Dalı
dc.identifier.yokid413086
dc.publisher.instituteFen Bilimleri Enstitüsü
dc.publisher.universityKOÇ ÜNİVERSİTESİ
dc.identifier.thesisid297799
dc.description.pages89
dc.publisher.disciplineDiğer


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