Arithmetic calculus of Fourier transforms by Igusa local zeta functions
HTML articles powered by AMS MathViewer
- by Tatsuo Kimura PDF
- Trans. Amer. Math. Soc. 346 (1994), 297-306 Request permission
Abstract:
We show the possibility of explicit calculation of the Fourier transforms of complex powers of relative invariants of some prehomogeneous vector spaces over $\mathbb {R}$ by using the explicit form of $p$-adic Igusa local zeta functions.References
-
A. Gyoja, Functional equations for Igusa local zeta functions, in preparation.
- Hiroshi Hosokawa, Some results on Igusa local zeta functions associated with simple prehomogeneous vector spaces, J. Math. Soc. Japan 49 (1997), no. 3, 565–587. MR 1452703, DOI 10.2969/jmsj/04930565
- Jun-ichi Igusa, Some results on $p$-adic complex powers, Amer. J. Math. 106 (1984), no. 5, 1013–1032. MR 761577, DOI 10.2307/2374271
- Jun-ichi Igusa, On functional equations of complex powers, Invent. Math. 85 (1986), no. 1, 1–29. MR 842045, DOI 10.1007/BF01388789
- Jun-ichi Igusa, On a certain class of prehomogeneous vector spaces, J. Pure Appl. Algebra 47 (1987), no. 3, 265–282. MR 910424, DOI 10.1016/0022-4049(87)90051-X
- Jun-ichi Igusa, Zeta distributions associated with some invariants, Amer. J. Math. 109 (1987), no. 1, 1–33. MR 878195, DOI 10.2307/2374548 K. Iwasawa, A note on $L$-functions, Proc. Internat. Congress Math. (Cambridge, Mass., 1950), vol. 1, Amer. Math. Soc., Providence, RI, 1952, p. 322; A letter to J. Dieudonné (1952), Appendix in Adv. Stud. Pure Math. 21 (1992).
- Tatsuo Kimura and Takeyoshi Kogiso, On adelic zeta functions of prehomogeneous vector spaces with finitely many adelic open orbits, Zeta functions in geometry (Tokyo, 1990) Adv. Stud. Pure Math., vol. 21, Kinokuniya, Tokyo, 1992, pp. 21–31. MR 1210781, DOI 10.2969/aspm/02110021
- T. Kimura, S. Kasai, and H. Hosokawa, Universal transitivity of simple and $2$-simple prehomogeneous vector spaces, Ann. Inst. Fourier (Grenoble) 38 (1988), no. 2, 11–41 (English, with French summary). MR 949009 M. Kashiwara, T. Kimura, and M. Muro, Microlocal calculus of Fourier transforms over $\mathbb {R}$, in preparation.
- Tatsuo Kimura, The $b$-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, Nagoya Math. J. 85 (1982), 1–80. MR 648417
- Masakazu Muro, Microlocal analysis and calculations on some relatively invariant hyperfunctions related to zeta functions associated with the vector spaces of quadratic forms, Publ. Res. Inst. Math. Sci. 22 (1986), no. 3, 395–463. MR 861776, DOI 10.2977/prims/1195177844
- Takashi Ono, An integral attached to a hypersurface, Amer. J. Math. 90 (1968), 1224–1236. MR 238851, DOI 10.2307/2373298
- Fumihiro Sat\B{o}, Zeta functions in several variables associated with prehomogeneous vector spaces. I. Functional equations, Tohoku Math. J. (2) 34 (1982), no. 3, 437–483. MR 676121, DOI 10.2748/tmj/1178229205
- Fumihiro Sat\B{o}, Zeta functions in several variables associated with prehomogeneous vector spaces. I. Functional equations, Tohoku Math. J. (2) 34 (1982), no. 3, 437–483. MR 676121, DOI 10.2748/tmj/1178229205
- M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J. 65 (1977), 1–155. MR 430336
- Mikio Sato and Takuro Shintani, On zeta functions associated with prehomogeneous vector spaces, Ann. of Math. (2) 100 (1974), 131–170. MR 344230, DOI 10.2307/1970844
- J. T. Tate, Fourier analysis in number fields, and Hecke’s zeta-functions, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 305–347. MR 0217026
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 346 (1994), 297-306
- MSC: Primary 11S40; Secondary 11S80, 20G20
- DOI: https://doi.org/10.1090/S0002-9947-1994-1267223-5
- MathSciNet review: 1267223