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On certain Ramanujan's modular equations of degree 7

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In this paper, we give alternative proofs of Ramanujan's modular equations of degree 7, by employing certain theta-function identities.

Abstract

In this paper, we give alternative proofs of Ramanujan's modular equations of degree 7, by employing certain theta-function identities.

참고문헌 (13)

  1. N. D. Baruah, "Certain Theta Function Identities and Ramanujan's Modular Equations of Degree 3", Indian J. Math, 48(1), pp.113~133 (2006)
  2. N. D. Baruah, "Ramanujan's Modular Equations of Degree 5", Proc. Indian Acad. Sci, 122(4), pp.485~506 (2012)
  3. B. C. Berndt, "Ramanujan's Notebooks" (1991), Springer
  4. Z.-G. Liu, "Some theta function Identities Associated with the Modular Equations of Degree 5", Elec. J. Comb. Num. Theory, 1, pp.1~14 (2001)
  5. Z.-G. Liu, "An Extension of the Quintuple Product Identity and its Applications", Pacific J. Math, 246(2), pp.89~134 (2010)
  6. S. Ramanujan, "Notebooks" (1957), Tata Institute of Fundamental Research
  7. S. Ramanujan, "The Lost Notebook and Other Unpublished Papers" (1988), Narosa
  8. L. Schlafli, "Beweis der Hermiteschen Verwandlungstafeln fur elliptischen modularfunction", J. Reine Angew. Math, 72, pp.360~369 (1870)
  9. H. Schroter, "De aequationibus modularibus, Dissertatio Inauguralis, Albertina Litterarum Universitate", Regiomonti, ~ (1854)
  10. L.-C. Shen, "On the modular equations of degree 3", Proc. Amer. Math. Soc, 122, pp.1101~1114 (1994)
  11. L.-C. Shen, "On Some Modular Equations of Degree 5", Proc. Amer. Math. Soc, 123, pp.1521~1526 (1995)
  12. K. R. Vasuki, "On Some Ramanujan's Schlafli Type Modular Equations", Aus. J. Math. Anal. Appl, 3(2), pp.1~8 (2006)
  13. K. R. Vasuki, "On Ramanujan's Modular Equation of Degree 7", J. Number Theory, 153, pp.304~308 (2015)

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