Euler's Function on Products of Primes in Progressions

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dc.contributor.authorFrancis, Forrest
dc.contributor.supervisorAkbary, Amir
dc.date.accessioned2018-01-22T17:46:32Z
dc.date.available2018-01-22T17:46:32Z
dc.date.issued2017
dc.degree.levelMastersen_US
dc.description.abstractIn 1962, Rosser and Schoenfeld asked whether there were infinitely many natural numbers n for which n/φ(n) > e^C log(log(n)), where C is the Euler-Mascheroni constant and φ(n) is Euler's totient function. This question was answered in the affirmative in 1983 by Jean-Louis Nicolas, who showed that there are infinitely many such n both in the case that the Riemann Hypothesis is true, and in the case that the Riemann Hypothesis is false. Landau's theorem naturally generalizes to the scenario where we restrict our attention to integers whose prime divisors all fall in a fixed arithmetic progression. In this thesis, I discuss the methods of Nicolas as they relate to the classical result, then turn my attention to answering the relevant analogue of Rosser and Schoenfeld's question for this restricted set of integers. It will be shown that, for certain arithmetic progressions, Nicolas' answer generalizes to a setting where the Generalized Riemann Hypothesis on a particular set of L-functions is concerned.en_US
dc.embargoNoen_US
dc.identifier.urihttps://hdl.handle.net/10133/5006
dc.language.isoen_USen_US
dc.proquest.subject0405en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Sciencesen_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.subjectResearch Subject Categories::MATHEMATICSen_US
dc.subjectEuler-Mascheroni constanten_US
dc.subjectLandau's theoremen_US
dc.subjectRiemann hypothesisen_US
dc.titleEuler's Function on Products of Primes in Progressionsen_US
dc.typeThesisen_US
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