Regularized orbital integrals for representations of

Author:
Jason Levy

Journal:
Trans. Amer. Math. Soc. **354** (2002), 2521-2539

MSC (2000):
Primary 22E30, 22E35

DOI:
https://doi.org/10.1090/S0002-9947-02-02967-7

Published electronically:
February 1, 2002

MathSciNet review:
1885662

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a finite-dimensional representation of , on a vector space defined over a local field of characteristic zero, we produce a regularization of orbital integrals and determine when the resulting distribution is non-trivial.

**1.**Borel, Armand; Harish-Chandra,*Arithmetic subgroups of algebraic groups*, Ann. of Math. (2)**75**(1962), 485-535. MR**26:5081****2.**Datskovsky, Boris; Wright, David J.,*The adelic zeta function associated to the space of binary cubic forms. II. Local theory*, J. Reine Angew. Math.**367**(1986), 27-75. MR**87m:11034****3.**Jacquet, H. and Langlands, R. P.,*Automorphic forms on*, Lecture Notes in Mathematics, Vol. 114, 1970. MR**53:5481****4.**G. Kempf,*Instability in invariant theory*, Annals of Math.**108**(1978), 299-316. MR**80c:20057****5.**Levy, J.,*Truncated integrals and the Shintani zeta function for the space of binary quartic forms*, Proc. Sympos. Pure Math., 66, Part 2 (1999), 277-300. MR**2001e:11039****6.**Rader, Cary; Rallis, Steve,*Spherical characters on**-adic symmetric spaces*, Amer. J. Math.**118**(1996), 91-178. MR**97c:22013****7.**Ranga Rao, R,*Orbital integrals in reductive groups*, Ann. of Math. (2)**96**(1972), 505-510. MR**47:8771****8.**Shintani, Takuro,*On Dirichlet series whose coefficients are class numbers of integral binary cubic forms*, J. Math. Soc. Japan**24**(1972), 132-188. MR**44:6619****9.**J. T. Tate,*Fourier analysis in number fields, and Hecke's zeta-functions,*, Algebraic Number Theory (1967), 305-347. MR**36:121****10.**Wright, David J.,*Twists of the Iwasawa-Tate zeta function*, Math. Z.**200**(1989), 209-231. MR**90c:11087**

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Additional Information

**Jason Levy**

Affiliation:
Department of Mathematics, University of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5, Canada

Email:
jlevy@science.uottawa.ca

DOI:
https://doi.org/10.1090/S0002-9947-02-02967-7

Received by editor(s):
August 7, 2000

Received by editor(s) in revised form:
September 11, 2001

Published electronically:
February 1, 2002

Additional Notes:
Partially supported by an NSERC grant.

Article copyright:
© Copyright 2002
American Mathematical Society