Institute of Natural and Mathematical Sciences
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Browsing Institute of Natural and Mathematical Sciences by Author "Cooper, Shaun"
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- ItemCubic elliptic functions(Massey University, 2003) Cooper, Shaun
- ItemThe development of elliptic functions according to Ramanujan and Venkatachaliengar(Massey University, 2000) Cooper, ShaunThese notes are based on the monograph Development of Elliptic Functions according to Ramanujan by K. Venkatachaliengar [2]. The goal of the notes is to show how some of the main properties of Jacobian and Weierstrass elliptic functions can be developed in an elementary way from the 1Ã1 function. All of the ideas presented in these notes can be found in Venkatachaliengar's book. The only thing I have done is to rearrange the order in which the material is presented. I am entirely responsible for any errors in these notes, and would be very grateful to be informed about them, whether they be large or small.
- ItemGeneral relations between sums of squares and sums of triangular numbers(Massey University, 2004) Chandrashekar, Adiga; Cooper, Shaun; Han, Jung HunLet = ( 1, · · · , m) be a partition of k. Let r (n) denote the number of solutions in integers of 1x21 + · · · + mx2 m = n, and let t (n) denote the number of solutions in non negative integers of 1x1(x1 +1)/2+· · ·+ mxm(xm +1)/2 = n. We prove that if 1 k 7, then there is a constant c , depending only on , such that r (8n + k) = c t (n), for all integers n.
- ItemOn the number of representations of certain integers as sums of eleven or thirteen squares(Massey University, 2002) Cooper, Shaun
- ItemOn the q-analogue of Kummer’s 24 solutions(Massey University, 2001) Cooper, ShaunThe 3φ2 transformations are used to derive q-analogues ofthe relations amongst Kummer’s 24 solutions.
