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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:
- [1]
- A Adolphson and S. Sperber, Exponential sums and Newton polyhedra\,\RM : cohomology and estimates, Ann. of Math. (2) \textbf{130} (1989), 367--406.
- [2]
- P. Deligne, La conjecture de Weil, Inst. Hautes \'Etudes Sci. Publ. Math. \textbf{48} (1974), 273--308.
- [3]
- P. Deligne, La conjecture de Weil. \RM {II}, Inst. Hautes \'Etudes Sci. Publ. Math. \textbf{52} (1980), 137--252.
- [4]
- J. Denef and F. Loeser, Weights of exponential sums, intersection cohomology, and Newton polyhedra, Invent. Math. \textbf{106} (1991), 275--294.
- [5]
- B. Dwork and F. Loeser, Hypergeometric series, Japanese J. Math. {\bf 19} (1993).
- [6]
- I. M. Gelfand, A. V. Zelevinskii, and M. M. Kapranov, Hypergeometric functions and toral manifolds, Funct. Anal. Appl. \textbf{23} (1989), 94--106.
- [7]
- I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Generalized Euler integrals and $\scr A$-hypergeometric functions, Adv. Math. \textbf{84} (1990), 255--271.
- [8]
- B. Gross and N. Koblitz, Gauss sums and the $p$-adic $\Gamma $-function, Ann. of Math. (2) \textbf{109} (1979), 569--581.
- [9]
- D. R. Heath-Brown, Cubic forms in ten variables, Proc. London Math. Soc. (3) \textbf{47} (1983), 225--257.
- [10]
- C. Hooley, On nonary cubic forms, J. Reine Angew. Math. \textbf{386} (1988), 32--98.
- [11]
- N. Katz, Sommes exponentielles, Ast\'erisque \textbf{79} (1980), 1--209.
- [12]
- H. D. Kloosterman, On the representation of numbers in the form $ax^2+by^2+cz^2+dt^2$, Acta Math. \textbf{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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