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Certain New Schläfli Type Mixed Modular Equations

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Bangalore University, Central College Campus, Bangalore, 560 001, Karnataka, India

    Megadahalli S. Mahadeva Naika & Manjunath Harish

  2. Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Peenya Campus, Peenya 4th Phase, Bengaluru, 560 058, Karnataka, India

    Sathyanarayana Chandankumar

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  1. Megadahalli S. Mahadeva Naika
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  2. Sathyanarayana Chandankumar
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  3. Manjunath Harish
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Correspondence to Megadahalli S. Mahadeva Naika.

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Mahadeva Naika, M.S., Chandankumar, S. & Harish, M. Certain New Schläfli Type Mixed Modular Equations. Vietnam J. Math. 44, 501–512 (2016). https://doi.org/10.1007/s10013-015-0162-y

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  • DOI: https://doi.org/10.1007/s10013-015-0162-y

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