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Further evaluations of Ramanujan-Weber class invariants $g_n$

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The purpose of this paper is to establish further evaluations of the class invariants gn using Ramanujan’s modular equations.

Abstract

The purpose of this paper is to establish further evaluations of the class invariants gn using Ramanujan’s modular equations.

참고문헌 (17)

  1. B. C. Berndt, "Ramanujan’s Notebooks, Part III" (1991), Springer-Verlag
  2. B. C. Berndt, "Ramanujan and the J-invariant", Canad. Math. Bull., 42, pp.427~440 (1999)
  3. B. C. Berndt, "Ramanujan’s class invariants and cubic continued fraction", Acta Arith., 72, pp.67~85 (1995)
  4. B. C. Berndt, "Ramanujan’s singular moduli", The Ramanujan J., 1, pp.53~74 (1997)
  5. B. C. Berndt, "Ramanujan’s class invariants with applications to the values of q-continued fractions and theta functions, in: Special Function, In Fields Institute Communication Series, 14", pp.37~53 (1997), AMS Providence. RI.
  6. B. J. Birch, "Weber’s class invariants", Mathematika, 16, pp.283~294 (1969)
  7. S. Bhargava, "Evaluations of Ramanujan-Weber class invariants gn", J. Indian Math. Soc., 72(1-4), pp.115~127 (2005)
  8. H. H. Chan, "Ramanujan’s Weber class invariants Gn and Watson’s empirical process", J. Londan Math. Soc., pp.545~561 (1998)
  9. D. A. Cox, "Primes of the form x2 + ny2" (1987), Wiley
  10. E. Konstantinou, , Computers and Mathematics with Applications, 59, pp.2901~2917 (2010)
  11. S. Lang, "Elliptic Functions" (1987), Springer
  12. S. Ramanujan, "Modular equations and approximations to π", Quart. J. Math, 45, pp.350~372 (1914)
  13. Notebooks (2 volumes), "S. Ramanujan", Tata Institute of Fundamental Research, ~ (1957)
  14. The lost notebook and other unpublished paper, "S. Ramanujan", Narosa, ~ (1988)
  15. G. N. Watson, "Some singular moduli (I)", Quart. J. Math., 3, pp.81~98 (1932)
  16. G. N.Watson, "Some singular moduli (II)", Quart. J. Math., 3, pp.189~212 (1932)
  17. H. Weber, "Lehrbuch der Algebra, III" (1908), Braunschweig

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