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Revisit to Ramanujan’s modular equations of degree 21

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Abstract

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.

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References

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Acknowledgement

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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Authors and Affiliations

  1. Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru, 570 006, India

    K. R. Vasuki, E. N. Bhuvan & T. Anusha

Authors
  1. K. R. Vasuki
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  2. E. N. Bhuvan
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  3. T. Anusha
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Correspondence to K. R. Vasuki, E. N. Bhuvan or T. Anusha.

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Vasuki, K.R., Bhuvan, E.N. & Anusha, T. Revisit to Ramanujan’s modular equations of degree 21. Indian J Pure Appl Math 50, 1097–1105 (2019). https://doi.org/10.1007/s13226-019-0376-x

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  • DOI: https://doi.org/10.1007/s13226-019-0376-x

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