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Book Review

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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

References [Enhancements On Off] (What's this?)

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  • 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 $p$-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 $p$-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, $B$-functions and holonomic systems (Rationality of $b$-functions), Invent. Math., 38 (1976), 33-53. MR 55:3309
  • 15. T. Kimura, The $b$-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 $p$-adic complex powers and $b$-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 $p$-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 $p$-adic complex power, Trans. Amer. Math. Soc., 278 (1983), 481-493. MR 84k:14019

Review Information:

Reviewer: Margaret Robinson
Affiliation: Mount Holyoke College
Email: robinson@mtholyoke.edu
Journal: Bull. Amer. Math. Soc. 38 (2001), 221-227
MSC (2000): Primary 11Sxx, 11S40, 11Mxx, 11Gxx, 14Gxx
Published electronically: December 27, 2000
Review copyright: © Copyright 2000 American Mathematical Society
American Mathematical Society