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Available in print format 		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): Bernard Dwork
Title: Generalized hypergeometric functions
Additional book information: Clarendon Press, Oxford, 1991, 188 pp. US$63.00. ISBN 0-19-853565-8.

References:

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A Adolphson and S. Sperber, Exponential sums and Newton polyhedra: cohomology and estimates, Ann. of Math. (2) 130 (1989), 367-406. MR 1014928 (91e:11094)

[2]
P. Deligne, La conjecture de Weil, Inst. Hautes Études Sci. Publ. Math. 48 (1974), 273-308. MR 0340258 (49:5013)

[3]
-, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137-252. MR 601520 (83c:14017)

[4]
J. Denef and F. Loeser, Weights of exponential sums, intersection cohomology, and Newton polyhedra, Invent. Math. 106 (1991), 275-294. MR 1128216 (93a:14019)

[5]
B. Dwork and F. Loeser, Hypergeometric series, Japanese J. Math. 19 (1993). MR 1231511 (95f:33013)

[6]
I. M. Gelfand, A. V. Zelevinskii, and M. M. Kapranov, Hypergeometric functions and toral manifolds, Funct. Anal. Appl. 23 (1989), 94-106. MR 1011353 (90m:22025)

[7]
I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Generalized Euler integrals and $ \mathcal{A}$-hypergeometric functions, Adv. Math. 84 (1990), 255-271. MR 1080980 (92e:33015)

[8]
B. Gross and N. Koblitz, Gauss sums and the p-adic $ \Gamma $-function, Ann. of Math. (2) 109 (1979), 569-581. MR 534763 (80g:12015)

[9]
D. R. Heath-Brown, Cubic forms in ten variables, Proc. London Math. Soc. (3) 47 (1983), 225-257. MR 703978 (85b:11025)

[10]
C. Hooley, On nonary cubic forms, J. Reine Angew. Math. 386 (1988), 32-98. MR 936992 (89h:11014)

[11]
N. Katz, Sommes exponentielles, Astérisque 79 (1980), 1-209. MR 617009 (82m:10059)

[12]
H. D. Kloosterman, On the representation of numbers in the form $ {ax^2} + {by^2} + {cz^2} + {dt^2}$, Acta Math. 49 (1926), 407-464.

Additional Information:

Reviewer(s):
Alan Adolphson

Review Information:
Journal: Bull. Amer. Math. Soc. 29 (1993), 279-282.
DOI: 10.1090/S0273-0979-1993-00419-1
PII: S 0273-0979(1993)00419-1




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