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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)
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- 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.
- B. J. Birch, "Weber’s class invariants", Mathematika, 16, pp.283~294 (1969)
- S. Bhargava, "Evaluations of Ramanujan-Weber class invariants gn", J. Indian Math. Soc., 72(1-4), pp.115~127 (2005)
- H. H. Chan, "Ramanujan’s Weber class invariants Gn and Watson’s empirical process", J. Londan Math. Soc., pp.545~561 (1998)
- D. A. Cox, "Primes of the form x2 + ny2" (1987), Wiley
- E. Konstantinou, , Computers and Mathematics with Applications, 59, pp.2901~2917 (2010)
- S. Lang, "Elliptic Functions" (1987), Springer
- S. Ramanujan, "Modular equations and approximations to π", Quart. J. Math, 45, pp.350~372 (1914)
- Notebooks (2 volumes), "S. Ramanujan", Tata Institute of Fundamental Research, ~ (1957)
- The lost notebook and other unpublished paper, "S. Ramanujan", Narosa, ~ (1988)
- G. N. Watson, "Some singular moduli (I)", Quart. J. Math., 3, pp.81~98 (1932)
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- H. Weber, "Lehrbuch der Algebra, III" (1908), Braunschweig
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