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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$89.95$
Scott Ahlgren, Bruce C. Berndt, Ae Ja Yee, and Alexandru Zaharescu, Integrals of Eisenstein series and derivatives of $L$-functions, Int. Math. Res. Not. 32 (2002), 1723–1738. MR 1916839, DOI 10.1155/S107379280211110X
George E. Andrews, On the theorems of Watson and Dragonette for Ramanujan’s mock theta functions, Amer. J. Math. 88 (1966), 454–490. MR 200258, DOI 10.2307/2373202
George E. Andrews, The theory of partitions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1998. Reprint of the 1976 original. MR 1634067
George E. Andrews, An introduction to Ramanujan’s “lost” notebook, Amer. Math. Monthly 86 (1979), no. 2, 89–108. MR 520571, DOI 10.2307/2321943
George E. Andrews, The hard-hexagon model and Rogers-Ramanujan type identities, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 9, 5290–5292. MR 629656, DOI 10.1073/pnas.78.9.5290
George E. Andrews, Ramanujan’s “lost” notebook. I. Partial $\theta$-functions, Adv. in Math. 41 (1981), no. 2, 137–172. MR 625891, DOI 10.1016/0001-8708(81)90013-X
George E. Andrews, Ramanujan’s “lost” notebook. I. Partial $\theta$-functions, Adv. in Math. 41 (1981), no. 2, 137–172. MR 625891, DOI 10.1016/0001-8708(81)90013-X
George E. Andrews, Ramanujan’s “lost” notebook. I. Partial $\theta$-functions, Adv. in Math. 41 (1981), no. 2, 137–172. MR 625891, DOI 10.1016/0001-8708(81)90013-X
George E. Andrews, Ramanujan’s “lost” notebook. IV. Stacks and alternating parity in partitions, Adv. in Math. 53 (1984), no. 1, 55–74. MR 748896, DOI 10.1016/0001-8708(84)90017-3
George E. Andrews, Unsolved Problems: Questions and Conjectures in Partition Theory, Amer. Math. Monthly 93 (1986), no. 9, 708–711. MR 1540966, DOI 10.2307/2322284
George E. Andrews, Ramanujan’s “lost” notebook. V. Euler’s partition identity, Adv. in Math. 61 (1986), no. 2, 156–164. MR 849849, DOI 10.1016/0001-8708(86)90072-1
George E. Andrews, Ramanujan’s “lost” notebook. VIII. The entire Rogers-Ramanujan function, Adv. Math. 191 (2005), no. 2, 393–407. MR 2103218, DOI 10.1016/j.aim.2004.03.012
George E. Andrews, Ramanujan’s “lost” notebook. IX. The partial theta function as an entire function, Adv. Math. 191 (2005), no. 2, 408–422. MR 2103219, DOI 10.1016/j.aim.2004.03.013
R. J. Baxter and George E. Andrews, Lattice gas generalization of the hard hexagon model. I. Star-triangle relation and local densities, J. Statist. Phys. 44 (1986), no. 1-2, 249–271. MR 854405, DOI 10.1007/BF01010916
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 (1986), no. 5-6, 713–728. MR 858255, DOI 10.1007/BF01011904
George E. Andrews and R. J. Baxter, Lattice gas generalization of the hard hexagon model. III. $q$-trinomial coefficients, J. Statist. Phys. 47 (1987), no. 3-4, 297–330. MR 894396, DOI 10.1007/BF01007513
George E. Andrews, Freeman J. Dyson, and Dean Hickerson, Partitions and indefinite quadratic forms, Invent. Math. 91 (1988), no. 3, 391–407. MR 928489, DOI 10.1007/BF01388778
George E. Andrews and F. G. Garvan, Ramanujan’s “lost” notebook. VI. The mock theta conjectures, Adv. in Math. 73 (1989), no. 2, 242–255. MR 987276, DOI 10.1016/0001-8708(89)90070-4
George E. Andrews and Dean Hickerson, Ramanujan’s “lost” notebook. VII. The sixth order mock theta functions, Adv. Math. 89 (1991), no. 1, 60–105. MR 1123099, DOI 10.1016/0001-8708(91)90083-J
A. O. L. Atkin and P. Swinnerton-Dyer, Some properties of partitions, Proc. London Math. Soc. (3) 4 (1954), 84–106. MR 60535, DOI 10.1112/plms/s3-4.1.84
Bruce C. Berndt, Ramanujan’s notebooks. Part I, Springer-Verlag, New York, 1985. With a foreword by S. Chandrasekhar. MR 781125, DOI 10.1007/978-1-4612-1088-7
Bruce C. Berndt, Ramanujan’s notebooks. Part II, Springer-Verlag, New York, 1989. MR 970033, DOI 10.1007/978-1-4612-4530-8
Bruce C. Berndt, Ramanujan’s notebooks. Part III, Springer-Verlag, New York, 1991. MR 1117903, DOI 10.1007/978-1-4612-0965-2
Bruce C. Berndt, Ramanujan’s notebooks. Part IV, Springer-Verlag, New York, 1994. MR 1261634, DOI 10.1007/978-1-4612-0879-2
Bruce C. Berndt, Ramanujan’s notebooks. Part V, Springer-Verlag, New York, 1998. MR 1486573, DOI 10.1007/978-1-4612-1624-7
Bruce C. Berndt and Robert A. Rankin (eds.), Ramanujan: essays and surveys, History of Mathematics, vol. 22, American Mathematical Society, Providence, RI; London Mathematical Society, London, 2001. MR 1862732, DOI 10.1090/hmath/022
H. Cohen, $q$-identities for Maass waveforms, Invent. Math. 91 (1988), no. 3, 409–422. MR 928490, DOI 10.1007/BF01388779
Freeman J. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635–652. MR 522147, DOI 10.1090/S0002-9904-1972-12971-9
Freeman J. Dyson, A walk through Ramanujan’s garden, Ramanujan revisited (Urbana-Champaign, Ill., 1987) Academic Press, Boston, MA, 1988, pp. 7–28. MR 938957
F. G. Garvan, New combinatorial interpretations of Ramanujan’s partition congruences mod $5,7$ and $11$, Trans. Amer. Math. Soc. 305 (1988), no. 1, 47–77. MR 920146, DOI 10.1090/S0002-9947-1988-0920146-8
G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work. , Chelsea Publishing Co., New York, 1959. MR 0106147
[32] G. H. Hardy and S. Ramanujan.
Asymptotic formulæin combinatory analysis.
Proc. London Math. Soc, 17:75-115, 1918.
J. Lepowsky and S. Milne, Lie algebraic approaches to classical partition identities, Adv. in Math. 29 (1978), no. 1, 15–59. MR 501091, DOI 10.1016/0001-8708(78)90004-X
I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. With contributions by A. Zelevinsky; Oxford Science Publications. MR 1354144
[35] Hans Rademacher.
On the partition function 
.
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.
Srinivasa Ramanujan, Notebooks. Vols. 1, 2, Tata Institute of Fundamental Research, Bombay, 1957. MR 0099904
Srinivasa Ramanujan, The lost notebook and other unpublished papers, Springer-Verlag, Berlin; Narosa Publishing House, New Delhi, 1988. With an introduction by George E. Andrews. MR 947735
G. N. Watson, The final problem: an account of the mock theta functions, Ramanujan: essays and surveys, Hist. Math., vol. 22, Amer. Math. Soc., Providence, RI, 2001, pp. 325–347. MR 1862757
[40] G. N. Watson.
The mock theta functions (2).
Proc. London Math. Soc. (2), 42:274-304, 1937.
- [1]
- S. Ahlgren, B. C. Berndt, A. J. Yee, and A. Zaharescu.
Integrals of Eisenstein series and derivatives of 
-functions.
Internat. Math. Res. Not., 2002:1723-1738, 2002. MR 1916839
- [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
- [3]
- George E. Andrews.
The Theory of Partitions.
Addison-Wesley, Reading, Mass., 1976;
reprinted, Cambridge University Press, 1998. MR 1634067
- [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
- [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
- [6]
- George E. Andrews.
Ramanujan's ``lost'' notebook. I. Partial 
-functions.
Adv. in Math., 41:137-172, 1981. MR 0625891
- [7]
- George E. Andrews.
Ramanujan's ``lost'' notebook. II. 
-function expansions.
Adv. in Math., 41:173-185, 1981. MR 0625891
- [8]
- George E. Andrews.
Ramanujan's ``lost'' notebook. III. The Rogers-Ramanujan continued fraction.
Adv. in Math., 41:186-208, 1981. MR 0625891
- [9]
- George E. Andrews.
Ramanujan's ``lost'' notebook. IV. Stacks and alternating parity in partitions.
Adv. in Math., 53:55-74, 1984. MR 0748896
- [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
- [12]
- George E. Andrews.
Ramanujan's ``lost'' notebook. VIII. The entire Rogers-Ramanujan function.
Adv. in Math., 191:393-407, 2005. MR 2103218
- [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
- [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
- [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
- [16]
- George E. Andrews and R. J. Baxter.
Lattice gas generalization of the hard hexagon model, III. 
-trinomial coefficients.
J. Statist. Phys., 47:297-330, 1987. MR 0894396
- [17]
- George E. Andrews, Freeman J. Dyson, and Dean Hickerson.
Partitions and indefinite quadratic forms.
Invent. Math., 91:391-407, 1988. MR 0928489
- [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
- [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
- [20]
- A. O. L. Atkin and P. Swinnerton-Dyer.
Some properties of partitions.
Proc. London Math. Soc. (3), 4:84-106, 1954. MR 0060535
- [21]
- Bruce C. Berndt.
Ramanujan's Notebooks, Part I.
Springer-Verlag, New York, 1985. MR 0781125
- [22]
- Bruce C. Berndt.
Ramanujan's Notebooks, Part II.
Springer-Verlag, New York, 1989. MR 0970033
- [23]
- Bruce C. Berndt.
Ramanujan's Notebooks, Part III.
Springer-Verlag, New York, 1991. MR 1117903
- [24]
- Bruce C. Berndt.
Ramanujan's Notebooks, Part IV.
Springer-Verlag, New York, 1994. MR 1261634
- [25]
- Bruce C. Berndt.
Ramanujan's Notebooks, Part V.
Springer-Verlag, New York, 1998. MR 1486573
- [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
- [27]
- Henri Cohen.
-identities for Maass waveforms.
Invent. Math., 91:409-422, 1988. MR 0928490
- [28]
- Freeman J. Dyson.
Missed opportunities.
Bull. Amer. Math. Soc., 78:635-652, 1972.
Gibbs Lecture of January 17, 1972. MR 0522147
- [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
- [30]
- F. G. Garvan.
New combinatorial interpretations of Ramanujan's partition congruences mod 
and 
.
Trans. Amer. Math. Soc., 305:47-77, 988. MR 0920146
- [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
- [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
- [34]
- I. G. Macdonald.
Symmetric Functions and Hall Polynomials.
Cambridge University Press, 1979.
Second edition, 1995. MR 1354144
- [35]
- Hans Rademacher.
On the partition function .
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
- [38]
- Srinivasa Ramanujan.
The Lost Notebook and Other Unpublished Papers.
Narosa, New Delhi, 1988. MR 0947735
- [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
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.
