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Book Information:
Author:
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 pp.,
ISBN 0-8218-2015-X,
$45.00$
1. M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math., 23 (1970), 145-150. MR 0256156
2. I. N. Bernstein and S. I. Gel'fand, Meromorphic property of the functions , Functional Anal. Appl., 3 (1969), 68-69. MR 0247457
3. I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl., 6 (1972), 273-285. MR 0320735
4. J. Denef, On the degree of Igusa's local zeta function, Amer. J. Math., 109 (1987), 991-1008. MR 0919001
5. J. Denef and D. Meuser, A functional equation of Igusa's local zeta functions, Amer. J. Math., 113 (1991), 1135-1152. MR 1137535
6. J. Denef, Report on Igusa's local zeta functions, Sém. Bourbaki 741 (1991), 1-25; Asterisque No. 201-203, 359-386. MR 1157848
7. I. M. Gel'fand and G. E. Shilov, Generalized functions. I, Academic Press (1964). MR 0166596
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 0347753; MR 53:8018
9. J. Igusa, Some results on -adic complex powers, Amer. J. Math., 106 (1984), 1013-1032. MR 0761577
10. J. Igusa, Zeta distributions associated with some invariants, Amer. J. Math., 109 (1987), 1-34. MR 0878195
11.J. Igusa, Universal -adic zeta functions and their functional equations, Amer. J. Math., 111 (1989), 671-716. MR 1020825
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 0430304
15. T. Kimura, The -functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, Nagoya Math. J., 85 (1982), 1-80. MR 0648417
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 1055652
17. N. Kurokawa, On the meromorphy of Euler Products (I), Proc. London Math. Soc. (3), 53 (1986), 1-47; (II), ibid., 209-236. MR 0842154; MR 88a:11084b
18. F. Loeser, Fonctions d'Igusa -adiques et polynômes de Bernstein, Amer. J. Math., 110 (1988), 1-22. MR 0926736
19. D. Meuser, On the poles of a local zeta function for curves, Invent. Math., 73 (1983), 445-465. MR 0718941
20. D. Meuser, On the degree of a local zeta function, Comp. Math., 62 (1987), 17-29. MR 0892148
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 0430336
22. L. Strauss, Poles of a two variable -adic complex power, Trans. Amer. Math. Soc., 278 (1983), 481-493. MR 0701506
- 1.
- M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math., 23 (1970), 145-150. MR 0256156
- 2.
- I. N. Bernstein and S. I. Gel'fand, Meromorphic property of the functions , Functional Anal. Appl., 3 (1969), 68-69. MR 0247457
- 3.
- I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl., 6 (1972), 273-285. MR 0320735
- 4.
- J. Denef, On the degree of Igusa's local zeta function, Amer. J. Math., 109 (1987), 991-1008. MR 0919001
- 5.
- J. Denef and D. Meuser, A functional equation of Igusa's local zeta functions, Amer. J. Math., 113 (1991), 1135-1152. MR 1137535
- 6.
- J. Denef, Report on Igusa's local zeta functions, Sém. Bourbaki 741 (1991), 1-25; Asterisque No. 201-203, 359-386. MR 1157848
- 7.
- I. M. Gel'fand and G. E. Shilov, Generalized functions. I, Academic Press (1964). MR 0166596
- 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 0347753; MR 53:8018
- 9.
- J. Igusa, Some results on -adic complex powers, Amer. J. Math., 106 (1984), 1013-1032. MR 0761577
- 10.
- J. Igusa, Zeta distributions associated with some invariants, Amer. J. Math., 109 (1987), 1-34. MR 0878195
- 11.
- J. Igusa, Universal -adic zeta functions and their functional equations, Amer. J. Math., 111 (1989), 671-716. MR 1020825
- 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 0430304
- 15.
- T. Kimura, The -functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, Nagoya Math. J., 85 (1982), 1-80. MR 0648417
- 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 1055652
- 17.
- N. Kurokawa, On the meromorphy of Euler Products (I), Proc. London Math. Soc. (3), 53 (1986), 1-47; (II), ibid., 209-236. MR 0842154; MR 88a:11084b
- 18.
- F. Loeser, Fonctions d'Igusa -adiques et polynômes de Bernstein, Amer. J. Math., 110 (1988), 1-22. MR 0926736
- 19.
- D. Meuser, On the poles of a local zeta function for curves, Invent. Math., 73 (1983), 445-465. MR 0718941
- 20.
- D. Meuser, On the degree of a local zeta function, Comp. Math., 62 (1987), 17-29. MR 0892148
- 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 0430336
- 22.
- L. Strauss, Poles of a two variable -adic complex power, Trans. Amer. Math. Soc., 278 (1983), 481-493. MR 0701506
Review Information:
Reviewer:
Margaret Robinson
Affiliation:
Mount Holyoke College
Email:
robinson@mtholyoke.edu
Journal:
Bull. Amer. Math. Soc.
38 (2001), 221-227
Published electronically:
December 27, 2000
Review copyright:
© Copyright 2000
American Mathematical Society