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Fundamental theorem of prehomogeneous vector spaces of characteristic p

Published online by Cambridge University Press:  17 April 2009

Tatsuo Kimura ,
Takeyoshi Kogiso  and
Makiko Fujinaga
Tatsuo Kimura
Affiliation:
Institute of MathematicsUniversity of Tsukuba, Ibaraki 305Japan
Takeyoshi Kogiso
Affiliation:
Institute of MathematicsUniversity of Tsukuba, Ibaraki 305Japan
Makiko Fujinaga
Affiliation:
Institute of MathematicsUniversity of Tsukuba, Ibaraki 305Japan
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Abstract

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For a local field of characteristic 0, the functional equations of zeta distributions of prehomogeneous vector spaces have been obtained by M. Sato, Shintani, Igusa, F. Sato and Gyoja. In this paper, we shall consider the case of local fields of characteristic p > 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 331 - 341
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Borel, A., Collected papers.Google Scholar
[2]Borel, A., Linear algebraic groups (2nd edition), Graduate texts in mathematics (Springer-Verlag, Berlin, Heidelberg, New York, 1991).CrossRefGoogle Scholar
[3]Bruhat, F. and Tits, J., ‘Groupes algebriques sur un corps local, Chapitre III, complements et applications a la cohomologie Galoisienne’, J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 34 (1987).Google Scholar
[4]Chen, Z., ‘Fonction zêta associée à un espace préhomogène et sommes de Gauss’.Google Scholar
[5]Chen, Z., ‘A classification of irreducible prehomogeneous vector spaces over an algebraically closed field of characteristic p (II)’, (in Chinese), Chinese Ann. Math. Ser. A. 9 (1988), p. 10–22.Google Scholar
[6]Gyoja, A., ‘Talk at 1993 JAMI conference’, Johns Hopkins University.Google Scholar
[7]Hironaka, H., ‘Resolution of singularities of an algebraic variety over a field of characteristic zero’, Ann. of Math 79 (1964), p. 109–326.CrossRefGoogle Scholar
[8]Igusa, J.-I., ‘Complex powers and asymptotic expansion I’, J. Reine Angew. Math 268/269 (1974), 110–130.Google Scholar
[9]Igusa, J.-I., ‘Complex powers and asymptotic expansion II’, J. Reine Angew.Math 278/279 (1975), 308–321.Google Scholar
[10]Igusa, J.-I., Lectures on forms of higher degree (Tata Inst. Fund. Research, Bombay, 1978).Google Scholar
[11]Igusa, J.-I., ‘Some results on p-adic complex powers’, Amer. J. Math 106 (1984), 1013–1032.CrossRefGoogle Scholar
[12]Igusa, J.-I., ‘Zeta distributions associated with some invariants’, Amer. J. Math 110 (1988), 197–233.CrossRefGoogle Scholar
[13]Igusa, J.-I., ‘Some observations on higher degree characters’, Amer. J. Math 99 (1977), 393–417.CrossRefGoogle Scholar
[14]Sato, F., ‘;Zeta functions in several variables associated with prehomogeneous vector spaces I: Functional equations’, Tôhoku Math. J. 34 (1982), 437–483.CrossRefGoogle Scholar
[15]Sato, F., ‘On functional equations of zeta distributions’, Adv. Stud. Pure Math. 15 (1989), 465–508.CrossRefGoogle Scholar
[16]Sato, M. and Kimura, T., ‘A classification of irreducible prehomogeneous vector spaces and their relative invariants’, Nagoya Math. J. 65 (1977), 1–155.CrossRefGoogle Scholar
[17]Sato, M. and Shintani, T., ‘On zeta functions associated with prehomogeneous vector spaces’, Ann. of Math 100 (1974), 131–170.CrossRefGoogle Scholar
[18]Serre, J.P., Cohomologie Galoisienne, Lecture Notes in Math. 5 (Springer-Verlag, Berlin, Heidelberg, New York, 1964).Google Scholar