## The development of the elliptic functions according to Ramanujan : a thesis presented in partial fulfillment of the requirements for the degree of Master of Information Sciences in Mathematics at Massey University

 dc.contributor.author Lam, Heung Yeung dc.date.accessioned 2017-09-28T01:47:46Z dc.date.available 2017-09-28T01:47:46Z dc.date.issued 2000 dc.description.abstract Srinivasa Ramanujan (1887-1920) was one of the world's greatest mathematical geniuses. He made substantial contributions to elliptic functions, continued fractions, infinite series, and the theory of numbers. For many years people have studied Ramanujan's work and tried to obtain a better understanding of his work. The main purpose of my thesis will be to consider some important classical results on elliptic functions and give proofs of these results using the methods which could have been used by Ramanujan. This will give an insight into how Ramanujan may have proved many of his results since his own proofs are often unknown. This thesis contains five chapters. Chapter 1 is the introduction and this is related to Chapter 2 up to Chapter 4. The goal for Chapter 2 is to write the transformation of S2n+1(q), Φr,s(q), U2n(q), and V2n(q) in terms of P(p), Q (p), and R(p). Chapter 3 discusses Ramanujan's congruence for partitions and we give a proof for Ramanujan's modulus 5 partition congruence. In Chapter 4, we investigate a method of determining the number of representations of an integer n as the sum of two, four, six, and eight squares and triangular numbers. Then we present two computer programs which are for the sums of squares and triangles. Finally, some interesting relations between the sums of squares and the sums of triangles are shown. en_US dc.identifier.uri http://hdl.handle.net/10179/12094 dc.language.iso en en_US dc.publisher Massey University en_US dc.rights The Author en_US dc.subject Elliptic functions en_US dc.subject Ramanujan Aiyangar, Srinivasa, 1887-1920 en_US dc.title The development of the elliptic functions according to Ramanujan : a thesis presented in partial fulfillment of the requirements for the degree of Master of Information Sciences in Mathematics at Massey University en_US dc.type Thesis en_US massey.contributor.author Lam, Heung Yeung thesis.degree.discipline Mathematics en_US thesis.degree.grantor Massey University en_US thesis.degree.level Masters en_US thesis.degree.name Master of Information Sciences (M. Inf. Sc.) en_US
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