By P. Deligne (auth.), Roger Howe (eds.)
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116 (1966), 279-309. [38] F. Sato, Zeta funetions in severa1 variables assoeiated with prehomogeneous veetor spaees. I, Tßhoku Math. J. 34 (1982), 437-483. [39] M. Sato and T. Shintani, On zeta funetions assoeiated with prehomogeneous veetor spaees, Ann. Math. 100 (1974), 131-170. [40] M. Sato and T. Kimura, A e1assifieation of irredueible prehomogeneous veetor spaees and their relative invariants, Nagoya Math. J. 65 (1977), 1-155. -P. Serre, Cohomo1ogie Ga1oisienne, Leet. Notes in Math. 5, Springer-Verlag (1965).
00. The asymptotic expansions in (ii), (iii) are both in terms of certain w's and their derivatives. p(w) is not holomorphic on Qa(Kx ) is finite. p(w) for each wluK is a rational function of t wen). p(w) in the s-plane are negative rational numbers. re known in analysis at least in The fact that the meromorphic continuation of =~. can be proved by using Hironaka's theorem on desingularization was discovered by Bernshtein-Gel'fand [4) and Atiyah [2); asymptotic expansion of Jeanquartier [20). p(i), F;(i*).
P. Langlands. Orbital integrals on forms of Math. 105 (1983), 465-506. SL(3). Amer. J. [24] L~ DUng Trang, Sur 1es noeuds a1gebriques, Comp. Math. 25 (1972), 281-321. [25] B. Lichtin, Some a1gebro-geometrie formu1ae for poles of If(x,y)l s , to appear in the Ameriean Journal of Mathematies. [26] A. Maeintyre, On definab1e subsets of p-adie fie1ds, J. Symb. Logie, 41 (1976), 605-610. [27] B. Malgrange, Integrales asymptotiques et monodromie, Ann. Ee. Norm. Sup. 7 (1974), 405-430. M. Mars, Les nombres de Tamagawa de eertains groupes exeeptionne1s, BuH.