Abstract
We give proofs for new Ramanujan-type modular equations discovered by M. Somos and establish applications of some of them.
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References
Baruah, N.D.: Modular equations for Ramanujan’s cubic continued fraction. J. Math. Anal. Appl. 268(1), 244–255 (2002)
Baruah, N.D.: On some of Ramanujan’s Schläfli-type “mixed” modular equations. J. Number Theory 100(2), 270–294 (2003)
Berndt, B.C.: Ramanujan’s Notebooks. Part III. Springer, New York (1991)
Berndt, B.C.: Ramanujan’s Notebooks. Part IV. Springer, New York (1994)
Mahadeva Naika, M.S.: A note on cubic modular equations of degree two. Tamsui Oxf. J. Math. Sci. 22(1), 1–8 (2006)
Mahadeva Naika, M.S., Chandan Kumar, S.: Some new Schläfli-type modular equations in quartic theory. In: Ramanujan Math. Soc. Lect. Notes Ser., vol. 14, pp. 185–199. Ramanujan Math. Soc., Mysore (2010)
Ramanujan, S.: Notebooks (2 Volumes). Tata Institute of Fundamental Research, Bombay (1957)
Somos, M.: Personal Communication
Vasuki, K.R.: On some of Ramanujan’s P–Q modular equations. J. Indian Math. Soc. 73(3–4), 131–143 (2006)
Vasuki, K.R., Sreeramamurthy, T.G.: A note on P–Q modular equations. Tamsui Oxf. J. Math. Sci. 21(2), 109–120 (2005)
Acknowledgements
The author would like to thank Bruce C. Berndt for his very helpful comments and encouragement and Micheal Somos for the useful communications. Also, the author is grateful to the referee who offered useful comments and suggestions.
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Yuttanan, B. New modular equations in the spirit of Ramanujan. Ramanujan J 29, 257–272 (2012). https://doi.org/10.1007/s11139-012-9399-1
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DOI: https://doi.org/10.1007/s11139-012-9399-1