JACOBI'S TWO-SQUARE AND FOUR-SQUARE THEOREMS VIA ROGER'S IDENTITY
Main Article Content
Abstract
We obtain Jacobi's two-square and four-square theorems as an application of an identity of L. J. Rogers.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
C. Adiga, B.C. Berndt, S. Bhargava and G.N. Watson, "Chapter 16 of Ramanujan's Second Note- book: Theta-functions and q-series", Mem. Amer. Math. Soc. 315, 53 (1985), p. 1-85.
G.E. Andrews, "Applications of Basic Hypergeometric Functions", S.l.A.M., Rev 16 (1974), p. 441-484.
S. Bhargava and Chandrashekar Adiga, "Simple Proofs of Jacobi's Two and Four Square Theo- rems", Int. J. Math. Educ. Sci Technol (U.K.) 1-3 (1988), p. 779-782.
E. Grosswald, "Representations of Integers as Sums of Squares", Springer- Verlag, New York (1985).
M.D. Hirschhorn, "A Simple Proof of Jacobi's Two Square Theorem", Amer. Math. Monthly 92 (1985), p. 579-580.
M.D. Hirschhorn, "A Simple Proof of Jacobi's Four Square Theorem", Proc. Amer. Math. Soc. 101 (1987), p. 436-438.
F. H. Jackson, "Summation of q-Hypergeometric Series", Mess. Math, 50 (1921), p. 101-112.
S. Ramanujan, "Notebooks (2 Volumes), Tata Institute of Fundamental Research", Bombay , (1957).
L. J. Rogers, "Third Memoir on the expansion of Certain Infinite Products", Proc. London Math. Soc. 26 (1895), p. 15-32.