Ramanujan's class invariants and cubic continued fraction

Bruce C. Berndt; Heng Huat Chan; Liang-Cheng Zhang

Acta Arithmetica (1995)

  • Volume: 73, Issue: 1, page 67-85
  • ISSN: 0065-1036

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Bruce C. Berndt, Heng Huat Chan, and Liang-Cheng Zhang. "Ramanujan's class invariants and cubic continued fraction." Acta Arithmetica 73.1 (1995): 67-85. <http://eudml.org/doc/206811>.

@article{BruceC1995,
author = {Bruce C. Berndt, Heng Huat Chan, Liang-Cheng Zhang},
journal = {Acta Arithmetica},
keywords = {Ramanujan's class invariants; modular equation; singular modulus; elliptic integrals; explicit formulae; Ramanujan's cubic continued fraction; class invariant formulae},
language = {eng},
number = {1},
pages = {67-85},
title = {Ramanujan's class invariants and cubic continued fraction},
url = {http://eudml.org/doc/206811},
volume = {73},
year = {1995},
}

TY - JOUR
AU - Bruce C. Berndt
AU - Heng Huat Chan
AU - Liang-Cheng Zhang
TI - Ramanujan's class invariants and cubic continued fraction
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 1
SP - 67
EP - 85
LA - eng
KW - Ramanujan's class invariants; modular equation; singular modulus; elliptic integrals; explicit formulae; Ramanujan's cubic continued fraction; class invariant formulae
UR - http://eudml.org/doc/206811
ER -

References

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  1. [1] B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1994. Zbl0785.11001
  2. [2] B. C. Berndt and H. H. Chan, Some values for the Rogers-Ramanujan continued fraction, Canad. J. Math. 20 (1995). Zbl0838.33011
  3. [3] B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's class invariants, Kronecker's limit formula, and modular equations, to appear. Zbl0885.11058
  4. [4] J. M. and P. B. Borwein, Pi and the AGM, Wiley, New York, 1987. 
  5. [5] G. S. Carr, Formulas and Theorems in Pure Mathematics, 2nd ed., Chelsea, New York, 1970. Zbl0209.00102
  6. [6] H. H. Chan, On Ramanujan's cubic continued fraction, Acta Arith., to appear. Zbl0834.11030
  7. [7] K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226. Zbl0535.10007
  8. [8] K. G. Ramanathan, On the Rogers-Ramanujan continued fraction, Proc. Indian Acad. Sci. Math. Sci. 93 (1984), 67-77. Zbl0565.10009
  9. [9] K. G. Ramanathan, Ramanujan's continued fraction, Indian J. Pure Appl. Math. 16 (1985), 695-724. Zbl0573.10001
  10. [10] K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89. Zbl0682.12002
  11. [11] S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372. Zbl45.1249.01
  12. [12] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957. 
  13. [13] S. Ramanujan, Collected Papers, Chelsea, New York, 1962. 
  14. [14] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. Zbl0639.01023
  15. [15] G. N. Watson, Theorems stated by Ramanujan (IX): two continued fractions, J. London Math. Soc. 4 (1929), 231-237. Zbl55.0274.01
  16. [16] G. N. Watson, Theorems stated by Ramanujan (XIV): a singular modulus, J. London Math. Soc. 6 (1931), 126-132. Zbl0003.12102
  17. [17] G. N. Watson, Some singular moduli (I), Quart. J. Math. 3 (1932), 81-98. Zbl0005.00902
  18. [18] G. N. Watson, Some singular moduli (II), Quart. J. Math. 3 (1932), 189-212. Zbl0005.29604
  19. [19] G. N. Watson, Singular moduli (3), Proc. London Math. Soc. 40 (1936), 83-142. 
  20. [20] G. N. Watson, Singular moduli (4), Acta Arith. 1 (1936), 284-323. Zbl0013.19603
  21. [21] G. N. Watson, Singular moduli (5), Proc. London Math. Soc. 42 (1937), 377-397. 
  22. [22] G. N. Watson, Singular moduli (6), Proc. London Math. Soc. 42 (1937), 398-409 
  23. [23] H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961. 

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