We obtain a modular transformation for the theta function
which enables us to unify and extend several modular transformations known in literature.
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References
S. Bhargava, “Unification of the cubic analogues of Jacobian theta functions,” J. Math. Anal. Appl., 193, 543–558 (1995).
M. D. Hirschhorn, F. G. Garvan, and J. M. Borwein, “Cubic analogues of the Jacobian theta functions θ(z, q) ,” Can. J., 45, 673–694 (1993).
S. Bhargava and S. N. Fathima, “Unification of modular transformations for cubic theta functions,” N. Z. J. Math., 33, 121–127 (2004).
S. Cooper, “Cubic theta functions,” J. Comput. Appl. Math., 160, 77–94 (2003).
S. Bhargava and N. Anitha, “A triple product identity for the three–parameter cubic theta function,” Indian J. Pure Appl. Math., 36, No. 9, 471–479 (2005).
C. Adiga, M. S. Mahadeva Naika, and J. H. Han, “General modular transformations for theta functions,” Indian J. Math., 49, No. 2, 239–251 (2007).
C. Adiga, B. C. Berndt, S. Bhargava, and G. N. Watson, “Chapter 16 of Ramanujan’s second notebook, theta functions and qseries,” Mem. Amer. Math. Soc., 53, No. 315 (1985).
J. M. Borwein and P. B. Borwein, “A cubic counterpart of Jacobi’s identity and the AGM,” Trans. Amer. Math. Soc., 323, 691–701 (1991).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 8, pp. 1040 – 1052, August, 2009.
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Bhargava, S., Mahadeva Naika, M.S. & Maheshkumar, M.C. A modular transformation for a generalized theta function with multiple parameters. Ukr Math J 61, 1233–1249 (2009). https://doi.org/10.1007/s11253-010-0273-2
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DOI: https://doi.org/10.1007/s11253-010-0273-2