Indian Journal of Pure and Applied Mathematics

, Volume 50, Issue 4, pp 1097–1105 | Cite as

Revisit to Ramanujan’s modular equations of degree 21

  • K. R. VasukiEmail author
  • E. N. BhuvanEmail author
  • T. AnushaEmail author


S. Ramanujan recorded six modular equations of degree 21 in his notebooks without recording proofs. B. C. Berndt proved all these modular equations by using the theory of modular forms. Recently Vasuki and Sharath proved two of them by using tools known to Ramanujan [5]. In this paper, we provide classical proof of remaining four identities.

Key words

Dedekind eta-function modular equation 


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The authors are grateful to the anonymous referees for their helpful comments and suggestions. T. Anusha is supported by grant No. 09/119(0202)/2017-EMR-1 by the funding agency Council of Scientific and Industrial Research (CSIR), India, under CSIR-JRF.


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Copyright information

© Indian National Science Academy 2019

Authors and Affiliations

  1. 1.Department of Studies in MathematicsUniversity of MysoreManasagangotri, MysuruIndia

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