Some identities on Schläfli-type mixed modular equations

B. R. Srivatsa Kumar, B. Sowmya Navada and Ranjani Nayak
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 1, Pages 86—91
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Authors and affiliations

B. R. Srivatsa Kumar
Department of Mathematics, Manipal Institute of Technology
Manial University, Manipal – 576 104, India

B. Sowmya Navada
Department of Sciences, Manipal University
Manipal – 576 104, India

Ranjani Nayak
Department of Sciences, Manipal University
Manipal – 576 104, India

Abstract

Srinivasa Ramanujan has recorded eleven Schläfli-type mixed modular equations on p. 86 of his first notebook. Using some of these in this paper, we obtain some new identities of the same type by using Maple.

Keywords

  • Theta-functions
  • Modular equations

AMS Classification

  • Primary: 11B65, 33D10
  • Secondary: 11F27

References

  1. Baruah, N. D. (2000) A few theta-function identities and some of Ramanujan’s modular equations, Ramanujan J., 4, 239–250.
  2. Baruah, N. D. (2003) On some of Ramanujan’s Schläfli-type mixed modular equations, J. Number Theory 100, 270–294. doi:10.1016/S0022-314X(02)00127-0.
  3. Berndt, B. C. (1991) Ramanujan’s Notebooks, Part III, Springer-Verlag, New York.
  4. Berndt, B. C. (1998) Ramanujan’s Notebooks, Part V, Springer-Verlag, New York.
  5. Ramanujan, S. Notebook’s (2 Volumes), Tata Institute of Fundamental Research, Bombay.
  6. Schläfli, L. (1870) Beweis der Hermiteschen Verwandlungstateln für elliptischen modular function, J. Reine Angew. Math. 72, 360–369.
  7. Vasuki, K. R. & T. G. Sreeramamurthy. (2005) Certain new Ramanujan’s Schläfli-type mixed modular equations. J. of Mathematical Analysis and Computation, 309, 238–255. doi:10.1016/j.jmaa.2005.01.035.

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Cite this paper

APA

Srivatsa Kumar, B. R., Sowmya Navada, B., & Nayak, R. (2015). Some identities on Schläfli-type mixed modular equations. Notes on Number Theory and Discrete Mathematics, 21(1), 86-91.

Chicago

Srivatsa Kumar, B. R., B. Sowmya Navada, and Ranjani Nayak. “Some Identities on Schläfli-type Mixed Modular Equations.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 86-91.

MLA

Srivatsa Kumar, B. R., B. Sowmya Navada, and Ranjani Nayak. “Some Identities on Schläfli-type Mixed Modular Equations.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 86-91. Print.

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