|
Shintani functions on 
Author:
Miki Hirano
Journal:
Trans. Amer. Math. Soc. 352 (2000), 1709-1721
MSC (1991):
Primary 11F70
Posted:
July 1, 1999
MathSciNet review:
1491868
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this paper, we give a formulation and an explicit formula for Shintani function on  , which has been studied by Murase and Sugano in the theory of automorphic  -functions. In particular, we obtain the multiplicity of this function.
- 1.
Arthur
Erdélyi, Wilhelm
Magnus, Fritz
Oberhettinger, and Francesco
G. Tricomi, Higher transcendental functions. Vols. I, II,
McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. Based, in
part, on notes left by Harry Bateman. MR 0058756
(15,419i)
- 2.
Flensted-Jensen, M., Spherical functions on a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal. 30 (1978), 106-146. MR 83f:43022
- 3.
Gerrit
Heckman and Henrik
Schlichtkrull, Harmonic analysis and special functions on symmetric
spaces, Perspectives in Mathematics, vol. 16, Academic Press
Inc., San Diego, CA, 1994. MR 1313912
(96j:22019)
- 4.
H.
Jacquet and R.
P. Langlands, Automorphic forms on 𝐺𝐿(2),
Lecture Notes in Mathematics, Vol. 114, Springer-Verlag, Berlin, 1970. MR 0401654
(53 #5481)
- 5.
Anthony
W. Knapp, Representation theory of semisimple groups,
Princeton Mathematical Series, vol. 36, Princeton University Press,
Princeton, NJ, 1986. An overview based on examples. MR 855239
(87j:22022)
- 6.
Atsushi
Murase and Takashi
Sugano, Shintani function and its application to automorphic
𝐿-functions for classical groups. I. The case of orthogonal
groups, Math. Ann. 299 (1994), no. 1,
17–56. MR
1273075 (96c:11054), http://dx.doi.org/10.1007/BF01459771
- 7.
Atsushi
Murase and Takashi
Sugano, Shintani functions and automorphic 𝐿-functions for
𝐺𝐿(𝑛), Tohoku Math. J. (2) 48
(1996), no. 2, 165–202. MR 1387815
(97i:11056), http://dx.doi.org/10.2748/tmj/1178225376
- 8.
Tsuzuki, M., Real Shintani Functions on
 , J. Math. Sci. Univ. Tokyo (to appear).
- 9.
J.-L.
Waldspurger, Correspondance de Shimura, J. Math. Pures Appl.
(9) 59 (1980), no. 1, 1–132 (French). MR 577010
(83f:10029)
- 10.
Hiroshi
Yamashita, Embeddings of discrete series into induced
representations of semisimple Lie groups. I. General theory and the case of
𝑆𝑈(2,2), Japan. J. Math. (N.S.) 16
(1990), no. 1, 31–95. MR 1064445
(92c:22032)
- 1.
- Erdélyi, A. et al., Higher transcendental functions I, McGraw-Hill, 1953. MR 15:419i
- 2.
- Flensted-Jensen, M., Spherical functions on a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal. 30 (1978), 106-146. MR 83f:43022
- 3.
- Heckman, G., Schlichtkrull, H., Harmonic analysis and special functions on symmetric spaces, Perspectives in Math., vol.16, Academic Press, 1994. MR 96j:22019
- 4.
- Jacquet, H., Langlands, R. P., Automorphic forms on
 , Lecture Note in Math., vol. 114, Springer-Verlag, 1970. MR 53:5481
- 5.
- Knapp, A. W., Representation Theory of Semisimple Groups; An Overview Based on Examples, Princeton Univ. Press, 1986. MR 87j:22022
- 6.
- Murase, A., Sugano, T., Shintani function and its application to automorphic L-function for classical groups (I. The case of orthogonal groups), Math. Ann. 299 (1994), 17-56. MR 96c:11054
- 7.
- -, Shintani functions and automorphic L-functions for
 , Tôhoku Math. J. 48 (1996), 165-202. MR 97i:11056
- 8.
- Tsuzuki, M., Real Shintani Functions on , J. Math. Sci. Univ. Tokyo (to appear).
- 9.
- Waldspurger, J. L., Correspondance de Shimura, J. Math. Pures Appl. (9) 59 (1980), 1-133. MR 83f:10029
- 10.
- Yamashita, H., Embeddings of discrete series into induced representations of semisimple Lie groups I -general theory and the case of
 , Japan J. Math. 16 (1990), 31-95. MR 92c:22032
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC (1991):
11F70
Retrieve articles in all journals
with MSC (1991):
11F70
Additional Information
Miki Hirano
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, 153, Japan
Email:
hirano@ms406ss5.ms.u-tokyo.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9947-99-02286-2
PII:
S 0002-9947(99)02286-2
Received by editor(s):
May 29, 1997
Received by editor(s) in revised form:
December 2, 1997
Posted:
July 1, 1999
Article copyright:
© Copyright 2000 American Mathematical Society
|
