Book Review
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MathSciNet review:
1568069
Full text of review:
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Book Information:
Author:
Bernard Dwork
Title:
Generalized hypergeometric functions
Additional book information:
Clarendon Press, Oxford, 1991, 188 pp. US$63.00. ISBN 0-19-853565-8.
Alan Adolphson and Steven Sperber, Exponential sums and Newton polyhedra: cohomology and estimates, Ann. of Math. (2) 130 (1989), no. 2, 367–406. MR 1014928, DOI 10.2307/1971424
Pierre Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307 (French). MR 340258
Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520
J. Denef and F. Loeser, Weights of exponential sums, intersection cohomology, and Newton polyhedra, Invent. Math. 106 (1991), no. 2, 275–294. MR 1128216, DOI 10.1007/BF01243914
B. Dwork and F. Loeser, Hypergeometric series, Japan. J. Math. (N.S.) 19 (1993), no. 1, 81–129. MR 1231511, DOI 10.4099/math1924.19.81
I. M. Gel′fand, A. V. Zelevinskiĭ, and M. M. Kapranov, Hypergeometric functions and toric varieties, Funktsional. Anal. i Prilozhen. 23 (1989), no. 2, 12–26 (Russian); English transl., Funct. Anal. Appl. 23 (1989), no. 2, 94–106. MR 1011353, DOI 10.1007/BF01078777
I. M. Gel′fand, M. M. Kapranov, and A. V. Zelevinsky, Generalized Euler integrals and $A$-hypergeometric functions, Adv. Math. 84 (1990), no. 2, 255–271. MR 1080980, DOI 10.1016/0001-8708(90)90048-R
Benedict H. Gross and Neal Koblitz, Gauss sums and the $p$-adic $\Gamma$-function, Ann. of Math. (2) 109 (1979), no. 3, 569–581. MR 534763, DOI 10.2307/1971226
D. R. Heath-Brown, Cubic forms in ten variables, Proc. London Math. Soc. (3) 47 (1983), no. 2, 225–257. MR 703978, DOI 10.1112/plms/s3-47.2.225
Christopher Hooley, On nonary cubic forms, J. Reine Angew. Math. 386 (1988), 32–98. MR 936992, DOI 10.1515/crll.1988.386.32
Nicholas M. Katz, Sommes exponentielles, Astérisque, vol. 79, Société Mathématique de France, Paris, 1980 (French). Course taught at the University of Paris, Orsay, Fall 1979; With a preface by Luc Illusie; Notes written by Gérard Laumon; With an English summary. MR 617009
[12] H. D. Kloosterman, On the representation of numbers in the form , Acta Math. 49 (1926), 407-464.
- [1]
- 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 -hypergeometric functions, Adv. Math. 84 (1990), 255-271. MR 1080980 (92e:33015)
- [8]
- B. Gross and N. Koblitz, Gauss sums and the p-adic -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 , Acta Math. 49 (1926), 407-464.
Review Information:
Reviewer:
Alan Adolphson
Journal:
Bull. Amer. Math. Soc.
29 (1993), 279-282
DOI:
https://doi.org/10.1090/S0273-0979-1993-00419-1