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A modular transformation for a generalized theta function with multiple parameters

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Ukrainian Mathematical Journal Aims and scope

We obtain a modular transformation for the theta function

$$ \sum\limits_{ - \infty }^\infty {\sum\limits_{ - \infty }^\infty {{q^{a\left( {{m^2} + mn} \right) + c{n^2} + \lambda m + \mu n + {\nu_\varsigma }Am + B{n_Z}Cm + Dn}}}, } $$

which enables us to unify and extend several modular transformations known in literature.

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References

  1. S. Bhargava, “Unification of the cubic analogues of Jacobian theta functions,” J. Math. Anal. Appl., 193, 543–558 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  2. 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).

    MATH  MathSciNet  Google Scholar 

  3. S. Bhargava and S. N. Fathima, “Unification of modular transformations for cubic theta functions,” N. Z. J. Math., 33, 121–127 (2004).

    MATH  MathSciNet  Google Scholar 

  4. S. Cooper, “Cubic theta functions,” J. Comput. Appl. Math., 160, 77–94 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  5. 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).

    MATH  MathSciNet  Google Scholar 

  6. 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).

    MATH  MathSciNet  Google Scholar 

  7. 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).

    MathSciNet  Google Scholar 

  8. 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).

    Article  MATH  MathSciNet  Google Scholar 

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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

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