An explicit version of Chebotarev's density theorem

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dc.contributor.authorDas, Sourabhashis
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorKadiri, Habiba
dc.contributor.supervisorNg, Nathan
dc.date.accessioned2021-01-15T16:41:04Z
dc.date.available2021-01-15T16:41:04Z
dc.date.issued2020
dc.degree.levelMastersen_US
dc.description.abstractChebotarev's density theorem generalizes the prime number theorem and Dirichlet's theorem for primes in arithmetic progressions to the setting of number fields. In particular, it asserts that prime ideals are equi-distributed over the conjugacy classes of the Galois group of any given normal extensions of number fields. The first part of the thesis investigates the works by Lagarias and Odlyzko together with the work of Winckler which provides an explicit error term for the prime counting function in Chebotarev's density theorem. We rework their argument and improve their bounds. The second part improves further by investigating more modern tools. Some of the main ideas are deriving an explicit formula for a smooth version of a certain prime counting function, and estimating associated sums over the zeros of Hecke L-functions.en_US
dc.identifier.urihttps://hdl.handle.net/10133/5825
dc.language.isoen_USen_US
dc.proquest.subjectComputer science [0984]en_US
dc.proquest.subjectApplied mathematics [0364]en_US
dc.proquest.subjectMathematics [0405]en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectAlgebraic number theoryen_US
dc.subjectAnalytic number theory, mathematical analysis and their applicationsen_US
dc.subjectChebotarev, N. G. (Nikolaĭ Grigorʹevich), 1894-1947en_US
dc.subjectDissertations, Academicen_US
dc.subjectLejeune Dirichlet, Peter Gustav, 1805-1859en_US
dc.subjectNumbers, Primeen_US
dc.titleAn explicit version of Chebotarev's density theoremen_US
dc.typeThesisen_US
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