On Ramanujan's quartic theory of elliptic functions

Journal of Number Theory

Volumn 88, Issue 1, 2001, Pages 129-156

  Berndt, Bruce C ^a   Chan, Heng Huat ^b   Liaw, Wen Chin ^c  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035343651     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.2000.2615     Document Type: Article

References (14)

1. 1. W. N. Bailey, "Generalized Hypergeometric Series," Cambridge University Press, Cambridge, UK, 1935; reprinted by Stechert-Hafher, New York, 1964.
2. 2. B. C. Berndt, "Ramanujan's Notebooks, Part II," Springer-Verlag, New York, 1989.
3. 3. B. C. Berndt, "Ramanujan's Notebooks, Part III," Springer-Verlag, New York, 1991.
4. 4. B. C. Berndt, "Ramanujan's Notebooks, Part V," Springer-Verlag, New York, 1998.
5. 5. B. C. Berndt, S. Bhargava, and F. G. Garvan, Ramanujan's theories of elliptic functions to alternative bases, Trans. Amer. Math. Soc. 347 (1995), 4163-4244.
6. 6. J. M. Borwein and P. B. Borwein, "Pi and the AGM," Wiley, New York, 1987.
7. 7. J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi's identity and the AGM, Trans. Amer. Math. Soc. 323 (1991), 691-701.
8. 8. H. H. Chan, W.-C. Liaw, and V. Tan, Ramanujan's class invariant λn and a new class of series for 1/π, J. London Math. Soc., to appear.
9. m2+mn+2n2, Proc. Amer. Math. Soc. 127 (1999), 1735-1744.
10. 10. W.-C. Liaw, "Contributions to Ramanujan's Theories of Modular Equations, Ramanujan-type Series for 1/π, and Partitions," Ph.D. thesis, University of Illinois, Urbana, IL, 1999.
11. 11. S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. 45 (1914), 350-372.
12. 12. S. Ramanujan, "Collected Papers," Cambridge University Press, Cambridge, UK, 1927; reprinted by Chelsea, New York, 1962; reprinted by the American Mathematical Society, Providence, RI, 2000.
13. 13. S. Ramanujan, "Notebooks," 2 vols., Tata Institute of Fundamental Research, Bombay, 1957.
14. 14. H. Weber, "Lehrbuch der Algebra," Bd. 3, Chelsea, New York, 1961.