Shintani functions on $GL(2,\mathbf {R})$
HTML articles powered by AMS MathViewer
- by Miki Hirano
- Trans. Amer. Math. Soc. 352 (2000), 1709-1721
- DOI: https://doi.org/10.1090/S0002-9947-99-02286-2
- Published electronically: July 1, 1999
- PDF | Request permission
Abstract:
In this paper, we give a formulation and an explicit formula for Shintani function on $GL(2,{\mathbf {R}})$, which has been studied by Murase and Sugano in the theory of automorphic $L$-functions. In particular, we obtain the multiplicity of this function.References
- Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
- Olga Taussky, An algebraic property of Laplace’s differential equation, Quart. J. Math. Oxford Ser. 10 (1939), 99–103. MR 83, DOI 10.1093/qmath/os-10.1.99
- 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
- H. Jacquet and R. P. Langlands, Automorphic forms on $\textrm {GL}(2)$, Lecture Notes in Mathematics, Vol. 114, Springer-Verlag, Berlin-New York, 1970. MR 0401654
- 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, DOI 10.1515/9781400883974
- 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, DOI 10.1007/BF01459771
- Atsushi Murase and Takashi Sugano, Shintani functions and automorphic $L$-functions for $\textrm {GL}(n)$, Tohoku Math. J. (2) 48 (1996), no. 2, 165–202. MR 1387815, DOI 10.2748/tmj/1178225376
- Tsuzuki, M., Real Shintani Functions on $SU(2,1)$, J. Math. Sci. Univ. Tokyo (to appear).
- J.-L. Waldspurger, Correspondance de Shimura, J. Math. Pures Appl. (9) 59 (1980), no. 1, 1–132 (French). MR 577010
- Hiroshi Yamashita, Embeddings of discrete series into induced representations of semisimple Lie groups. I. General theory and the case of $\textrm {SU}(2,2)$, Japan. J. Math. (N.S.) 16 (1990), no. 1, 31–95. MR 1064445, DOI 10.4099/math1924.16.31
Bibliographic Information
- Miki Hirano
- Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, 153, Japan
- MR Author ID: 601430
- Email: hirano@ms406ss5.ms.u-tokyo.ac.jp
- Received by editor(s): May 29, 1997
- Received by editor(s) in revised form: December 2, 1997
- Published electronically: July 1, 1999
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 1709-1721
- MSC (1991): Primary 11F70
- DOI: https://doi.org/10.1090/S0002-9947-99-02286-2
- MathSciNet review: 1491868