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Book Information:

Authors: George E. Andrews and Bruce C. Berndt
Title: Ramanujan's lost notebook, Part I
Additional book information: Springer, New York, 2005, xiv+437 pp., ISBN 0-387-25529-X, US$89.95

References [Enhancements On Off] (What's this?)

  • [1] S. Ahlgren, B. C. Berndt, A. J. Yee, and A. Zaharescu.
    Integrals of Eisenstein series and derivatives of $ L$-functions.
    Internat. Math. Res. Not., 2002:1723-1738, 2002. MR 1916839 (2003f:11056)
  • [2] George E. Andrews.
    On the theorems of Watson and Dragonette for Ramanujan's mock theta functions.
    Amer. J. Math., 88:454-490, 1966. MR 0200258 (34:157)
  • [3] George E. Andrews.
    The Theory of Partitions.
    Addison-Wesley, Reading, Mass., 1976;
    reprinted, Cambridge University Press, 1998. MR 1634067 (99c:11126)
  • [4] George E. Andrews.
    An introduction to Ramanujan's ``lost'' notebook.
    Amer. Math. Monthly, 86:89-108, 1979.
    Reprinted in [], pp. 165-184. MR 0520571 (80e:01018)
  • [5] George E. Andrews.
    The hard-hexagon model and Rogers-Ramanujan type identities.
    Proc. Nat. Acad. Sci. U.S.A., 78:5290-5292, 1981. MR 0629656 (82m:82005)
  • [6] George E. Andrews.
    Ramanujan's ``lost'' notebook. I. Partial $ \theta $-functions.
    Adv. in Math., 41:137-172, 1981. MR 0625891 (83m:10034a)
  • [7] George E. Andrews.
    Ramanujan's ``lost'' notebook. II. $ \vartheta $-function expansions.
    Adv. in Math., 41:173-185, 1981. MR 0625892 (83m:10034b)
  • [8] George E. Andrews.
    Ramanujan's ``lost'' notebook. III. The Rogers-Ramanujan continued fraction.
    Adv. in Math., 41:186-208, 1981. MR 0625893 (83m:10034c)
  • [9] George E. Andrews.
    Ramanujan's ``lost'' notebook. IV. Stacks and alternating parity in partitions.
    Adv. in Math., 53:55-74, 1984. MR 0748896 (85m:11062)
  • [10] George E. Andrews.
    Questions and conjectures in partition theory.
    Amer. Math. Monthly, 93:708-711, 1986. MR 1540966
  • [11] George E. Andrews.
    Ramanujan's ``lost'' notebook. V. Euler's partition identity.
    Adv. in Math., 61:156-164, 1986. MR 0849849 (87i:11137)
  • [12] George E. Andrews.
    Ramanujan's ``lost'' notebook. VIII. The entire Rogers-Ramanujan function.
    Adv. in Math., 191:393-407, 2005. MR 2103218 (2005h:11230)
  • [13] George E. Andrews.
    Ramanujan's ``lost'' notebook. IX. The partial theta function as an entire function.
    Adv. in Math., 191:408-422, 2005. MR 2103219 (2005h:11231)
  • [14] George E. Andrews and R. J. Baxter.
    Lattice gas generalization of the hard hexagon model, I. Star-triangle relation and local densities.
    J. Statist. Phys., 44:249-271, 1986. MR 0854405 (87i:82093)
  • [15] George E. Andrews and R. J. Baxter.
    Lattice gas generalization of the hard hexagon model, II. The local densities as elliptic functions.
    J. Statist. Phys., 44:713-728, 1986. MR 0858255 (88i:82063)
  • [16] George E. Andrews and R. J. Baxter.
    Lattice gas generalization of the hard hexagon model, III. $ q$-trinomial coefficients.
    J. Statist. Phys., 47:297-330, 1987. MR 0894396 (88h:82069)
  • [17] George E. Andrews, Freeman J. Dyson, and Dean Hickerson.
    Partitions and indefinite quadratic forms.
    Invent. Math., 91:391-407, 1988. MR 0928489 (89f:11071)
  • [18] George E. Andrews and F.G. Garvan.
    Ramanujan's ``lost'' notebook. VI. The mock theta conjectures.
    Adv. in Math., 73:242-255, 1989. MR 0987276 (90d:11115)
  • [19] George E. Andrews and Dean Hickerson.
    Ramanujan's ``lost'' notebook. VII. The sixth order mock theta functions.
    Adv. in Math., 89:60-105, 1991. MR 1123099 (92i:11027)
  • [20] A. O. L. Atkin and P. Swinnerton-Dyer.
    Some properties of partitions.
    Proc. London Math. Soc. (3), 4:84-106, 1954. MR 0060535 (15:685d)
  • [21] Bruce C. Berndt.
    Ramanujan's Notebooks, Part I.
    Springer-Verlag, New York, 1985. MR 0781125 (86c:01062)
  • [22] Bruce C. Berndt.
    Ramanujan's Notebooks, Part II.
    Springer-Verlag, New York, 1989. MR 0970033 (90b:01039)
  • [23] Bruce C. Berndt.
    Ramanujan's Notebooks, Part III.
    Springer-Verlag, New York, 1991. MR 1117903 (92j:01069)
  • [24] Bruce C. Berndt.
    Ramanujan's Notebooks, Part IV.
    Springer-Verlag, New York, 1994. MR 1261634 (95e:11028)
  • [25] Bruce C. Berndt.
    Ramanujan's Notebooks, Part V.
    Springer-Verlag, New York, 1998. MR 1486573 (99f:11024)
  • [26] Bruce C. Berndt and Robert A. Rankin, editors.
    Ramanujan: Essays and Surveys, volume 22 of History of Mathematics.
    American Mathematical Society and London Mathematical Society, Providence, RI, 2001. MR 1862732 (2003a:01024)
  • [27] Henri Cohen.
    $ q$-identities for Maass waveforms.
    Invent. Math., 91:409-422, 1988. MR 0928490 (89f:11072)
  • [28] Freeman J. Dyson.
    Missed opportunities.
    Bull. Amer. Math. Soc., 78:635-652, 1972.
    Gibbs Lecture of January 17, 1972. MR 0522147 (58:25442)
  • [29] Freeman J. Dyson.
    A walk through Ramanujan's garden.
    In Ramanujan Revisited, pages 7-28. Academic Press, Boston, 1988.
    Reprinted in [], pp. 261-275. MR 0938957 (89f:01065)
  • [30] F. G. Garvan.
    New combinatorial interpretations of Ramanujan's partition congruences mod $ 5,7$ and $ 11$.
    Trans. Amer. Math. Soc., 305:47-77, 988. MR 0920146 (89b:11081)
  • [31] G. H. Hardy.
    Ramanujan: Twelve lectures on subjects suggested by his life and work.
    AMS Chelsea, Providence, RI, 1999.
    Fourth printing, with additional corrections and comments. MR 0106147 (21:4881)
  • [32] G. H. Hardy and S. Ramanujan.
    Asymptotic formulæin combinatory analysis.
    Proc. London Math. Soc, 17:75-115, 1918.
  • [33] J. Lepowsky and S. Milne.
    Lie algebraic approaches to classical partition identities.
    Adv. in Math., 29:15-59, 1978. MR 0501091 (82f:17005)
  • [34] I. G. Macdonald.
    Symmetric Functions and Hall Polynomials.
    Cambridge University Press, 1979.
    Second edition, 1995. MR 1354144 (96h:05207)
  • [35] Hans Rademacher.
    On the partition function $ p(n)$.
    Proc. London Math. Soc. (2), 43:241-254, 1937.
  • [36] Srinivasa Ramanujan.
    Collected Papers.
    Cambridge University Press, 1927.
    Reprinted by Chelsea, New York, 1962. Reprinted by the American Mathematical Society, Providence, RI, 2000.
  • [37] Srinivasa Ramanujan.
    Notebooks, volumes 1 & 2.
    Tata Institute of Fundamental Research, Bombay, 1957. MR 0099904 (20:6340)
  • [38] Srinivasa Ramanujan.
    The Lost Notebook and Other Unpublished Papers.
    Narosa, New Delhi, 1988. MR 0947735 (89j:01078)
  • [39] G. N. Watson.
    The final problem: An account of the mock theta functions.
    J. London Math. Soc., 11:55-80, 1936.
    Reprinted in [], pp. 325-347. MR 1862757
  • [40] G. N. Watson.
    The mock theta functions (2).
    Proc. London Math. Soc. (2), 42:274-304, 1937.

Review Information:

Reviewer: David M. Bressoud
Affiliation: Macalester College
Email: bressoud@macalester.edu
Journal: Bull. Amer. Math. Soc. 43 (2006), 585-591
MSC (2000): Primary 11Fxx; Secondary 11A55, 11P55, 11P82, 11P83, 33D15
Published electronically: April 20, 2006
Review copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
American Mathematical Society