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Book Review
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Book Information
Author(s):
Jun-ichi Igusa
Title:
An introduction to the theory of local zeta functions
Additional book information:
American Mathematical Society,
Providence, RI, and International Press, Cambridge, MA,
2000,
xii + 232,
$45.00,
0-8218-2015-X
References:
-
- 1.
- M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math., 23 (1970), 145-150. MR 41:815
- 2.
- I. N. Bernstein and S. I. Gel'fand, Meromorphic property of the functions
, Functional Anal. Appl., 3 (1969), 68-69. MR 40:723 - 3.
- I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl., 6 (1972), 273-285. MR 47:9269
- 4.
- J. Denef, On the degree of Igusa's local zeta function, Amer. J. Math., 109 (1987), 991-1008. MR 89d:11108
- 5.
- J. Denef and D. Meuser, A functional equation of Igusa's local zeta functions, Amer. J. Math., 113 (1991), 1135-1152. MR 93e:11145
- 6.
- J. Denef, Report on Igusa's local zeta functions, Sém. Bourbaki 741 (1991), 1-25; Asterisque No. 201-203, 359-386. MR 93g:11119
- 7.
- I. M. Gel'fand and G. E. Shilov, Generalized functions. I, Academic Press (1964). MR 29:3869
- 8.
- J. Igusa, Complex powers and asymptotic expansions. I, J. Reine Angew. Math. 268/269 (1974), 110-130; II, ibid., 278/279 (1975), 307-321. MR 50:254; MR 53:8018
- 9.
- J. Igusa, Some results on
-adic complex powers, Amer. J. Math., 106 (1984), 1013-1032. MR 86f:11046 - 10.
- J. Igusa, Zeta distributions associated with some invariants, Amer. J. Math., 109 (1987), 1-34. MR 89h:11075
- 11.
- J. Igusa, Universal
-adic zeta functions and their functional equations, Amer. J. Math., 111 (1989), 671-716. MR 91e:11142 - 12.
- J. Igusa, On local zeta functions, Amer. Math. Soc. Transl. (2) 172, (1996), 1-20. CMP 96:11
- 13.
- J. Igusa, An Introduction to the Theory of Local Zeta Functions, AMS/IP Studies in Mathematics, 14, American Mathematical Society, Providence, RI; International Press, Cambridge, MA, 2000. CMP 2000:09
- 14.
- M. Kashiwara,
-functions and holonomic systems (Rationality of -functions), Invent. Math., 38 (1976), 33-53. MR 55:3309 - 15.
- T. Kimura, The
-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, Nagoya Math. J., 85 (1982), 1-80. MR 84j:32017 - 16.
- T. Kimura, F. Sato, and X.-W. Zhu, On the poles of
-adic complex powers and -functions of prehomogeneous vector spaces, Amer. J. Math., 112 (1990), 423-437. MR 91i:11171 - 17.
- N. Kurokawa, On the meromorphy of Euler Products (I), Proc. London Math. Soc. (3), 53 (1986), 1-47; (II), ibid., 209-236. MR 88a:11084a; MR 88a:11084b
- 18.
- F. Loeser, Fonctions d'Igusa
-adiques et polynômes de Bernstein, Amer. J. Math., 110 (1988), 1-22. MR 89d:11110 - 19.
- D. Meuser, On the poles of a local zeta function for curves, Invent. Math., 73 (1983), 445-465. MR 85i:14014
- 20.
- D. Meuser, On the degree of a local zeta function, Comp. Math., 62 (1987), 17-29. MR 88i:11093
- 21.
- M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65 (1977), 1-155. MR 55:3341
- 22.
- L. Strauss, Poles of a two variable
-adic complex power, Trans. Amer. Math. Soc., 278 (1983), 481-493. MR 84k:14019
Additional Information:
Reviewer(s):
Margaret
Robinson
Affiliation:
Mount Holyoke College
Email:
robinson@mtholyoke.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
38
(2001),
221-227.
MSC
(2000):
Primary 11Sxx, 11S40, 11Mxx, 11Gxx, 14Gxx
DOI:
10.1090/S0273-0979-00-00896-X
PII:
S 0273-0979(00)00896-X
Posted:
December 27, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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