Piatetski-shapir prime number theorem and chebotarev density theorem

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buir.advisorGüloğlu, Ahmet Muhtar
dc.contributor.authorAkbal, Yıldırım
dc.date.accessioned2016-05-03T08:52:18Z
dc.date.available2016-05-03T08:52:18Z
dc.date.copyright2015-07
dc.date.issued2015-07
dc.date.submitted29-07-2015
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (leaves 39-40).en_US
dc.descriptionThesis (Ph. D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2015.en_US
dc.description.abstractLet K be a nite Galois extension of the eld Q of rational numbers. In this thesis, we derive an asymptotic formula for the number of the Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincide with any given conjugacy class in the Galois group of K=Q. Applying this theorem to appropriate eld extensions, we conclude that there are in nitely many Piatetski-Shapiro primes lying in a given arithmetic progresion and furthermore there are in nitely many primes that can be expressed as a sum of a square and a xed positive integer multiple of another square.en_US
dc.description.provenanceSubmitted by Betül Özen (ozen@bilkent.edu.tr) on 2016-05-03T08:52:18Z No. of bitstreams: 1 YildirimakbalPhD10082319.pdf: 389144 bytes, checksum: 9232078e0c425988641274cdaf83f2c5 (MD5)en
dc.description.provenanceMade available in DSpace on 2016-05-03T08:52:18Z (GMT). No. of bitstreams: 1 YildirimakbalPhD10082319.pdf: 389144 bytes, checksum: 9232078e0c425988641274cdaf83f2c5 (MD5) Previous issue date: 2015-07en
dc.description.statementofresponsibilityby Yıldırım Akbal.en_US
dc.format.extentiv, 40 leaves : charts.en_US
dc.identifier.itemidB150930
dc.identifier.urihttp://hdl.handle.net/11693/29039
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectChebotarev density theoremen_US
dc.subjectPiatetski-Shapiro prime number theoremen_US
dc.subjectExponential sums over idealsen_US
dc.titlePiatetski-shapir prime number theorem and chebotarev density theoremen_US
dc.title.alternativePiatetski-shapiro asal sayı teoremi ve chebotarev yoğunluk teoremi.en_US
dc.typeThesisen_US
thesis.degree.disciplineMathematics
thesis.degree.grantorBilkent University
thesis.degree.levelDoctoral
thesis.degree.namePh.D. (Doctor of Philosophy)

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