Regularized orbital integrals for representations of
Author:
Jason Levy
Journal:
Trans. Amer. Math. Soc. 354 (2002), 25212539
MSC (2000):
Primary 22E30, 22E35
Published electronically:
February 1, 2002
MathSciNet review:
1885662
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Given a finitedimensional 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 nontrivial.
 1.
Armand
Borel and HarishChandra,
Arithmetic subgroups of algebraic groups, Ann. of Math. (2)
75 (1962), 485–535. MR 0147566
(26 #5081)
 2.
Boris
Datskovsky and David
J. Wright, The adelic zeta function associated to the space of
binary cubic forms. II. Local theory, J. Reine Angew. Math.
367 (1986), 27–75. MR 839123
(87m:11034), http://dx.doi.org/10.1515/crll.1986.367.27
 3.
H.
Jacquet and R.
P. Langlands, Automorphic forms on 𝐺𝐿(2),
Lecture Notes in Mathematics, Vol. 114, SpringerVerlag, BerlinNew York,
1970. MR
0401654 (53 #5481)
 4.
George
R. Kempf, Instability in invariant theory, Ann. of Math. (2)
108 (1978), no. 2, 299–316. MR 506989
(80c:20057), http://dx.doi.org/10.2307/1971168
 5.
Jason
Levy, Truncated integrals and the Shintani zeta function for the
space of binary quartic forms, Automorphic forms, automorphic
representations, and arithmetic (Fort Worth, TX, 1996) Proc. Sympos. Pure
Math., vol. 66, Amer. Math. Soc., Providence, RI, 1999,
pp. 277–299. MR 1703763
(2001e:11039)
 6.
Cary
Rader and Steve
Rallis, Spherical characters on 𝔭adic symmetric
spaces, Amer. J. Math. 118 (1996), no. 1,
91–178. MR
1375304 (97c:22013)
 7.
R.
Ranga Rao, Orbital integrals in reductive groups, Ann. of
Math. (2) 96 (1972), 505–510. MR 0320232
(47 #8771)
 8.
Takuro
Shintani, On Dirichlet series whose coefficients are class numbers
of integral binary cubic forms, J. Math. Soc. Japan
24 (1972), 132–188. MR 0289428
(44 #6619)
 9.
J.
T. Tate, Fourier analysis in number fields, and Hecke’s
zetafunctions, Algebraic Number Theory (Proc. Instructional Conf.,
Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 305–347.
MR
0217026 (36 #121)
 10.
David
J. Wright, Twists of the IwasawaTate zeta function, Math. Z.
200 (1989), no. 2, 209–231. MR 978295
(90c:11087), http://dx.doi.org/10.1007/BF01230282
 1.
 Borel, Armand; HarishChandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485535. 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), 2775. 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), 299316. 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), 277300. MR 2001e:11039
 6.
 Rader, Cary; Rallis, Steve, Spherical characters on adic symmetric spaces, Amer. J. Math. 118 (1996), 91178. MR 97c:22013
 7.
 Ranga Rao, R, Orbital integrals in reductive groups, Ann. of Math. (2) 96 (1972), 505510. 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), 132188. MR 44:6619
 9.
 J. T. Tate, Fourier analysis in number fields, and Hecke's zetafunctions,, Algebraic Number Theory (1967), 305347. MR 36:121
 10.
 Wright, David J., Twists of the IwasawaTate zeta function, Math. Z. 200 (1989), 209231. MR 90c:11087
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC (2000):
22E30,
22E35
Retrieve articles in all journals
with MSC (2000):
22E30,
22E35
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:
http://dx.doi.org/10.1090/S0002994702029677
PII:
S 00029947(02)029677
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
