q-series in number theory and combinatorics : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand

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dc.contributor.authorLam, Heung Yeung
dc.date.accessioned2010-07-21T02:00:32Z
dc.date.availableNO_RESTRICTIONen_US
dc.date.available2010-07-21T02:00:32Z
dc.date.issued2006
dc.description.abstractSrinivasa Ramanujan (1887-1920) was one of the world's greatest mathematical geniuses. He work extensively in a branch of mathematics called "q-series". Around 1913, he found an important formula which now is known as Ramanujan's 1ψ1summation formula. The aim of this thesis is to investigate Ramanujan's 1ψ1summation formula and explore its applications to number theory and combinatorics. First, we consider several classical important results on elliptic functions and then give new proofs of these results using Ramanujan's 1ψ1 summation formula. For example, we will present a number of classical and new solutions for the problem of representing an integer as sums of squares (one of the most celebrated in number theory and combinatorics) in this thesis. This will be done by using q-series and Ramanujan's 1ψ1 summation formula. This in turn will give an insight into how Ramanujan may have proven many of his results, since his own proofs are often unknown, thereby increasing and deepening our understanding of Ramanujan's work.en_US
dc.identifier.urihttp://hdl.handle.net/10179/1477
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectSrinivasa Ramanujanen_US
dc.subjectSummation formulaen_US
dc.subjectElliptic functionsen_US
dc.subjectMathematical transformationsen_US
dc.subject.otherFields of Research::230000 Mathematical Sciences::230100 Mathematics::230102 Number theory and field theoryen_US
dc.titleq-series in number theory and combinatorics : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealanden_US
dc.typeThesisen_US
massey.contributor.authorLam, Heung Yeung
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
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