Some results on Igusa local zeta functions associated with simple prehomogeneous vector spaces

Hiroshi HOSOKAWA

doi:10.2969/jmsj/04930565

Hiroshi HOSOKAWA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 3 Pages 565-587

DOI https://doi.org/10.2969/jmsj/04930565

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Published: 1997 Received: August 26, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : Igusa-1) J.-I. Igusa, On the arithmetic of a singular invariant, Amer. J. Math., 110 (1988), 197-233.
Igusa-2) J.-I. Igusa, B-functions and p-adic integrals, Algebraic Analysis, Papers Dedicated to Professor Sato Mikio on his Sixtieth Birthday, vol. 1, Academic Press (1988), 231-341.
Igusa-3) J.-I. Igusa, On functional equations of complex powers, Invent. Math., 85 (1986), 1-29.
Igusa-4) J.-I. Igusa, Some results on p-adic complex powers, Amer. J. Math., 106 (1984), 1013-1032.
Kasai) S. Kasai, On the b-functions of regular prehomogeneous vector spaces of simple algebraic groups, (in Japanese) R.I.M.S. KOKYUROKU, 629 (1987), 31-81.
Kimura-1) T. Kimura, Arithmetic calculus of Fourier transforms by Igusa local zeta functions, preprint.
Kimura-2) T. Kimura, Complex powers on p-adic fields and a resolution of singularities, Algebraic Analysis, Papers Dedicated to Professor Sato Mikio on his Sixtieth Birthday, vol. 1, Academic Press (1988), 345-355.
Kimura-3) T. Kimura, A classification of prehomogeneous vector spaces of simple algebraic groups with scalar multiplications, J. Algebra, 83 (1983), 72-100.
Kimura-4) T. Kimura, The b-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, Nagoya Math. J., 85 (1982), 1-80.
K-K-H) T. Kimura, S. Kasai and H. Hosokawa, Universal transitivity of simple and 2-simple prehomogeneous vector spaces, Ann. Inst. Fourier, 38-2 (1988), 11-41.
K-K) T. Kimura and T. Kogiso, On allelic zeta functions of prehomogeneous vector spaces with a finitely many open orbits, Advanced Studies in Pure Mathematics, 21 (1992), 21-31.
Tate) J. Tate, Fourier analysis in number fields and Hecke's zeta functions, Thesis Princeton, (1950); Algebraic number theory, Academic Press, (1967), 305-347.
F. Sato) F. Sato, On functional equations of zeta distributions, Advanced Studies in Pure Mathematics, 15 (1989), 465-508.
S-K) M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65 (1977), 1-155.

Right : [Igusa-1] J. -I. Igusa, On the arithmetic of a singular invariant, Amer. J. Math., 110 (1988), 197-233.
[Igusa-2] J. -I. Igusa, B-functions and p-adic integrals, Algebraic Analysis, Papers Dedicated to Professor Sato Mikio on his Sixtieth Birthday, vol. 1, Academic Press (1988), 231-341.
[Igusa-3] J. -I. Igusa, On functional equations of complex powers, Invent. Math., 85 (1986), 1-29.
[Igusa-4] J. -I. Igusa, Some results on p-adic complex powers, Amer. J. Math., 106 (1984), 1013-1032.
[Kasai] S. Kasai, On the b-functions of regular prehomogeneous vector spaces of simple algebraic groups, (in Japanese) R. I. M. S. KOKYUROKU, 629 (1987), 31-81.
[Kimura-1] T. Kimura, Arithmetic calculus of Fourier transforms by Igusa local zeta functions, preprint.
[Kimura-2] T. Kimura, Complex powers on p-adic fields and a resolution of singularities, Algebraic Analysis, Papers Dedicated to Professor Sato Mikio on his Sixtieth Birthday, vol. 1, Academic Press (1988), 345-355.
[Kimura-3] T. Kimura, A classification of prehomogeneous vector spaces of simple algebraic groups with scalar multiplications, J. Algebra, 83 (1983), 72-100.
[Kimura-4] T. Kimura, The b-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, Nagoya Math. J., 85 (1982), 1-80.
[K-K-H] T. Kimura, S. Kasai and H. Hosokawa, Universal transitivity of simple and 2-simple prehomogeneous vector spaces, Ann. Inst. Fourier, 38-2 (1988), 11-41.
[K-K] T. Kimura and T. Kogiso, On adelic zeta functions of prehomogeneous vector spaces with a finitely many open orbits, Advanced Studies in Pure Mathematics, 21 (1992), 21-31.
[Tate] J. Tate, Fourier analysis in number fields and Hecke's zeta functions, Thesis Princeton, (1950); Algebraic number theory, Academic Press, (1967), 305-347.
[F. Sato] F. Sato, On functional equations of zeta distributions, Advanced Studies in Pure Mathematics, 15 (1989), 465-508.
[S-K] M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65 (1977), 1-155.

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