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ArticleOriginal scientific text

Title

Ramanujan's class invariants and cubic continued fraction

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.
  2. School of Mathematics, Institute For Advanced Study, Princeton, New Jersey 08540, U.S.A.
  3. Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804, U.S.A.

Bibliography

  1. B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1994.
  2. B. C. Berndt and H. H. Chan, Some values for the Rogers-Ramanujan continued fraction, Canad. J. Math. 20 (1995).
  3. B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's class invariants, Kronecker's limit formula, and modular equations, to appear.
  4. J. M. and P. B. Borwein, Pi and the AGM, Wiley, New York, 1987.
  5. G. S. Carr, Formulas and Theorems in Pure Mathematics, 2nd ed., Chelsea, New York, 1970.
  6. H. H. Chan, On Ramanujan's cubic continued fraction, Acta Arith., to appear.
  7. K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226.
  8. K. G. Ramanathan, On the Rogers-Ramanujan continued fraction, Proc. Indian Acad. Sci. Math. Sci. 93 (1984), 67-77.
  9. K. G. Ramanathan, Ramanujan's continued fraction, Indian J. Pure Appl. Math. 16 (1985), 695-724.
  10. K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89.
  11. S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372.
  12. S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
  13. S. Ramanujan, Collected Papers, Chelsea, New York, 1962.
  14. S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
  15. G. N. Watson, Theorems stated by Ramanujan (IX): two continued fractions, J. London Math. Soc. 4 (1929), 231-237.
  16. G. N. Watson, Theorems stated by Ramanujan (XIV): a singular modulus, J. London Math. Soc. 6 (1931), 126-132.
  17. G. N. Watson, Some singular moduli (I), Quart. J. Math. 3 (1932), 81-98.
  18. G. N. Watson, Some singular moduli (II), Quart. J. Math. 3 (1932), 189-212.
  19. G. N. Watson, Singular moduli (3), Proc. London Math. Soc. 40 (1936), 83-142.
  20. G. N. Watson, Singular moduli (4), Acta Arith. 1 (1936), 284-323.
  21. G. N. Watson, Singular moduli (5), Proc. London Math. Soc. 42 (1937), 377-397.
  22. G. N. Watson, Singular moduli (6), Proc. London Math. Soc. 42 (1937), 398-409
  23. H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961.
Acta Arithmetica
1995/73/1
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Pages:
67-85
Main language of publication
English
Received
1995-01-08
Accepted
1995-02-13
Published
1995
Exact and natural sciences