The correction factor in Artin type problems

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dc.contributor.authorFakhari, Milad
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorAkbary-Majdabadno, Amir
dc.date.accessioned2021-12-02T18:51:28Z
dc.date.available2021-12-02T18:51:28Z
dc.date.issued2021
dc.degree.levelMastersen_US
dc.description.abstractIn 1927, Emil Artin conjectured a product expression for the density of primes p for which a given non-zero integer a is a primitive root modulo p. The conjectured density was proved in 1967 by Hooley under the assumption of the Generalized Riemann Hypothesis. In 2014, Lenstra, Moree, and Stevenhagen introduced a method involving character sums to deduce the formula for the product in the density for Artin’s conjecture. The method applies in similar problems such as the density of primes of cyclic reduction for Serre curves. In this thesis, we introduce a generalization of this method which yields product expressions for a large family of problems that can be stated by summations involving the orders of certain finite groups. As a consequence, the product expressions of some Artin type problems, such as the Titchmarsh Divisor Problem in Kummer families for primes in a given arithmetic progression, are computed here.en_US
dc.identifier.urihttps://hdl.handle.net/10133/6100
dc.language.isoen_USen_US
dc.proquest.subject0280en_US
dc.proquest.subject0405en_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.subjectnumber theoryen_US
dc.subjectcharacter sums methoden_US
dc.subjectdensity theoremsen_US
dc.subjectprimes in congruence classesen_US
dc.subjectalgebraic number theoryen_US
dc.subjectNumber theoryen_US
dc.subjectAlgebraic number theoryen_US
dc.subjectNumbers, Primeen_US
dc.subjectDissertations, Academicen_US
dc.titleThe correction factor in Artin type problemsen_US
dc.typeThesisen_US
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