Topics in explicit number theory

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dc.contributor.authorHasanalizade, Elchin
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorKadiri, Habiba
dc.contributor.supervisorNg, Nathan
dc.date.accessioned2023-09-26T19:51:33Z
dc.date.available2023-09-26T19:51:33Z
dc.date.issued2023
dc.degree.levelPh.D
dc.description.abstractThis doctoral thesis is made up of a collection of papers of the author. All of these papers are already published. The structure of this thesis is as follows. After the introduction, there are four chapters. In Chapters 2 and 3, we obtain explicit bounds for the number of non-trivial zeros of the Riemann zeta function and Dedekind zeta functions, which improve previous results of Trudgian. This improvement is based on ideas from previous works of Bennett et al., Kadiri and Ng and Trudgian. This is a joint work with Quanli Shen and Peng-Jie Wong. In Chapter 4, we apply explicit results from transcendental number theory due to Bugeaud, Laurent and Matveev to completely solve a Diophantine inequality involving the Fibonacci numbers and to study a particular case of the Terai-Shinsho conjecture. In Chapter 5, using elementary methods and explicit bounds for primes in arithmetic progressions due to Bennett et al. we study two Diophantine equations which involve multiplicative functions.
dc.identifier.urihttps://hdl.handle.net/10133/6588
dc.language.isoen
dc.proquest.subject0280
dc.proquest.subject0405
dc.proquestyesYes
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science
dc.publisher.departmentDepartment of Mathematics and Computer Science
dc.publisher.facultyArts and Science
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)
dc.subjectNumber theory
dc.subjectZeros of zeta functions
dc.subjectLinear forms in logarithms
dc.subjectDiophantine equations
dc.subjectMultiplicative functions
dc.subject.lcshFunctions, Zeta
dc.subject.lcshLogarithms
dc.subject.lcshTranscendental numbers
dc.subject.lcshDissertations, Academic
dc.titleTopics in explicit number theory
dc.typeThesis
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