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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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Book Information

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


References:

[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.


Additional Information:

Reviewer(s):
David M. Bressoud
Affiliation: Macalester College
Email: bressoud@macalester.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 43 (2006), 585-591.

MSC (2000): Primary 11Fxx; Secondary 11A55, 11P55, 11P82, 11P83, 33D15
PII: S 0273-0979(06)01110-4
Posted: April 20, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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