dc.contributor.author Lam, Heung Yeung dc.date.accessioned 2010-07-21T02:00:32Z dc.date.available NO_RESTRICTION en_US dc.date.available 2010-07-21T02:00:32Z dc.date.issued 2006 dc.identifier.uri http://hdl.handle.net/10179/1477 dc.description.abstract Srinivasa 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.language.iso en en_US dc.publisher Massey University en_US dc.rights The Author en_US dc.subject Srinivasa Ramanujan en_US dc.subject Summation formula en_US dc.subject Elliptic functions en_US dc.subject Mathematical transformations en_US dc.subject.other Fields of Research::230000 Mathematical Sciences::230100 Mathematics::230102 Number theory and field theory en_US dc.title 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 en_US dc.type Thesis en_US thesis.degree.discipline Mathematics en_US thesis.degree.grantor Massey University en_US thesis.degree.level Doctoral en_US thesis.degree.level Doctoral en thesis.degree.name Doctor of Philosophy (Ph.D.) en_US
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