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Classical approach to Ramanujan’s modular equations of septic degree

  • K. R. VasukiEmail author
  • Mahadevaswamy
Article
  • 29 Downloads

Abstract

In this paper, we prove six Ramanujan’s modular equations of septic degree by employing Ramanujan’s \(_1\psi _1\) summation formula and certain theta function identities.

Keywords

Ramanujan’s general theta function Modular equation 

Mathematics Subject Classification

11F20 33C05 

Notes

Acknowledgements

Authors would like to thank the anonymous referee for the valuable comments.

References

  1. 1.
    Berndt, B.C.: Ramanujan’s Notebooks, Part III. Springer, New York (1991)CrossRefGoogle Scholar
  2. 2.
    Liu, Z.-G.: An extension of the quintuple product identity and its applications. Pac. J. Math. 246, 345–390 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ramanujan, S.: Notebooks, vol. 2. Tata Institute of Fundamental Research, Bombay (1957)zbMATHGoogle Scholar
  4. 4.
    Vasuki, K.R., Veeresha, R.G.: On Ramanujan’s modular equation of degree 7. J. Number Theory 153, 304–308 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Vasuki, K.R., Veeresha, R.G.: Ramanujan’s Eisenstein series of level 7 and 14. J. Number Theory 159, 59–75 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Studies in MathematicsUniversity of MysoreMysoreIndia
  2. 2.Department of MathematicsNational Institute of EngineeringMysoreIndia

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