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Some new Ramanujan-type modular equations of degree 15

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Abstract

Ramanujan in his notebook recorded two modular equations involving multipliers with moduli of degrees (1,7) and (1,23). In this paper, we find some new Ramanujan-type modular equations involving multipliers with moduli of degrees (3,5) and (1,15), and give concise proofs by employing Ramanujan’s multiplier functional equation.

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References

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Acknowledgements

The authors would like to thank the anonymous referee for his helpful comments and invaluable suggestions.

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Authors and Affiliations

  1. College of Geography and Environmental Science, Henan University, No. 379, Mingli Road North, Zhengzhou, 450046, Henan, China

    Zhang Chuan-Ding & Yang Li

  2. Henan Technology Innovation Center of Spatio-Temporal Big Data, Henan University, No. 379, Mingli Road North, Zhengzhou, 450046, Henan, China

    Zhang Chuan-Ding & Yang Li

Authors
  1. Zhang Chuan-Ding
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  2. Yang Li
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Contributions

CDZ contributed to the conception and proof, LY performed the validation and writing. They reviewed the manuscript.

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Correspondence to Zhang Chuan-Ding.

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This work was supported by the National Natural Science Foundation of China (Grant No. 42174037).

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Chuan-Ding, Z., Li, Y. Some new Ramanujan-type modular equations of degree 15. Ramanujan J 64, 143–151 (2024). https://doi.org/10.1007/s11139-023-00817-y

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  • DOI: https://doi.org/10.1007/s11139-023-00817-y

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