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dc.contributor.authorCamire, Patrice 17:42:21 (GMT) 17:42:21 (GMT)
dc.description.abstractIf we fix an integer a not equal to -1 and which is not a perfect square, we are interested in estimating the quantity N_{a}(x) representing the number of prime integers p up to x such that a is a generator of the cyclic group (Z/pZ)*. We will first show how to obtain an aymptotic formula for N_{a}(x) under the assumption of the generalized Riemann hypothesis. We then investigate the average behaviour of N_{a}(x) and we provide an unconditional result. Finally, we discuss how to generalize the problem over (Z/mZ)*, where m > 0 is not necessarily a prime integer. We present an average result in this setting and prove the existence of oscillation.en
dc.publisherUniversity of Waterlooen
dc.subjectArtin's primitive root conjectureen
dc.subjectAverage result and composite modulien
dc.titleArtin's Primitive Root Conjecture and its Extension to Compositie Modulien
dc.typeMaster Thesisen
dc.subject.programPure Mathematicsen Mathematicsen
uws-etd.degreeMaster of Mathematicsen

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