Abstract
We consider three-variable analogues of the theta series of Borwein and Borwein. We prove various identities involving these theta series including a generalization of the cubic identity of Borwein and Borwein.
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References
S. Bhargava, “Unification of the cubic analogues of the Jacobian theta-function,” J. Math. Anal. Appl. 193 (1995), 543–558.
J.M. Borwein and P.B. Borwein, “A cubic counterpart of Jacobi’s identity and the AGM,” Trans. Amer. Math. Soc. 323 (1991), 691–701.
J.M. Borwein, P.B. Borwein, and F.G. Garvan, “Some cubic modular identities of Ramanujan,” Trans. Amer. Math. Soc. 343 (1994), 35–47.
M. Hirschhorn, F. Garvan, and J. Borwein, “Cubic analogues of the Jacobian theta function θ (z, q),” Canad. J. Math. 45 (1993), 673–694.
P. Solé, “D4, E6, E8 and the AGM”, Springer Lecture Notes in Computer Science 948 (1995), 448–455.
P. Solé and P. Loyer, “Un lattices, construction B, and AGM iterations,” European J. Combin. 19 (1998), 227–236.
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Chapman, R. Cubic Identities for Theta Series in Three Variables. Ramanujan J 8, 459–465 (2005). https://doi.org/10.1007/s11139-005-0273-2
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DOI: https://doi.org/10.1007/s11139-005-0273-2