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Ukrainian Mathematical Journal

, Volume 61, Issue 8, pp 1233–1249 | Cite as

A modular transformation for a generalized theta function with multiple parameters

  • S. Bhargava
  • M. S. Mahadeva Naika
  • M. C. Maheshkumar
Article
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.

Keywords

Simple Consequence Auxiliary Function Theta Function Simple Fact Function Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • S. Bhargava
    • 1
  • M. S. Mahadeva Naika
    • 2
  • M. C. Maheshkumar
    • 2
  1. 1.University of MysoreMysoreIndia
  2. 2.Bangalore UniversityBangaloreIndia

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