Ramanujan's class invariants and cubic continued fraction

• Autorzy: Bruce C. Berndt , Heng Huat Chan , Liang-Cheng Zhang
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 73
• Numer: 1
• Strony: 67-85

Daty

wydano

1995

otrzymano

1995-01-08

poprawiono

1995-02-13

Twórcy

autor

Bruce C. Berndt

• Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.

autor

Heng Huat Chan

• School of Mathematics, Institute For Advanced Study, Princeton, New Jersey 08540, U.S.A.

autor

Liang-Cheng Zhang

• Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804, U.S.A.

Bibliografia

• [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• [14] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.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.