Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 501–512 | Cite as

Certain New Schläfli Type Mixed Modular Equations

  • Megadahalli S. Mahadeva Naika
  • Sathyanarayana Chandankumar
  • Manjunath Harish
Article
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Abstract

Schläfli (J. Reine Angew. Math. 72, 360–369, 1870) has established modular equations involving k k ′ and λ λ ′ for degrees 3, 5, 7, 9, 11, 13, 17, and 19. On pages 86 and 88 of his first notebook, Ramanujan recorded 11 Schläfli-type modular equations for composite degrees. In this paper, we establish several new Schläfli type mixed modular equations for composite degrees by elementary algebraic manipulations which are analogous to those recorded by Ramanujan.

Keywords

Modular equations Theta-functions 

Mathematics Subject Classification (2010)

33D10 11A55 11F27 
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Notes

Acknowledgments

The authors are grateful to the referee for their valuable remarks and suggestions which considerably improved the quality of the paper. The first author is thankful to Department of Science and Technology (DST), New Delhi, India for support under the research project SR/S4/MS:739/11.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  • Megadahalli S. Mahadeva Naika
    • 1
  • Sathyanarayana Chandankumar
    • 2
  • Manjunath Harish
    • 1
  1. 1.Department of MathematicsBangalore UniversityBangaloreIndia
  2. 2.Department of MathematicsM. S. Ramaiah University of Applied SciencesBengaluruIndia

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