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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 842806, 33 pages
http://dx.doi.org/10.1155/2011/842806
Research Article

Shintani Functions on 𝑆 𝐿 ( 3 , 𝐑 )

Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153-8914, Japan

Received 25 May 2011; Revised 26 September 2011; Accepted 26 September 2011

Academic Editor: Andrei Volodin

Copyright © 2011 Keiju Sono. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Shintani, “On an explicit formula for class one “Whittaker functions” on GLn over ß-adic fields,” Proceedings of the Japan Academy, vol. 52, no. 4, pp. 180–182, 1976. View at Publisher · View at Google Scholar
  2. A. Murase and T. Sugano, “Shintani functions and automorphic L-functions for GL(n),” The Tohoku Mathematical Journal, vol. 48, no. 2, pp. 165–202, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. Murase and T. Sugano, “Shintani function and its application to automorphic L-functions for classical groups. I. The case of orthogonal groups,” Mathematische Annalen, vol. 299, no. 1, pp. 17–56, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  4. M. Hirano, “Shintani functions on GL(2,R),” Transactions of the American Mathematical Society, vol. 352, no. 4, pp. 1709–1721, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Hirano, “Shintani functions on GL(2,C),” Transactions of the American Mathematical Society, vol. 353, no. 4, pp. 1535–1550, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Tsuzuki, “Real Shintani functions and multiplicity free property for the symmetric pair (SU(1,1),S(U(1,1)×U(1))),” Journal of Mathematical Sciences The University of Tokyo, vol. 4, no. 3, pp. 663–727, 1997. View at Google Scholar · View at Zentralblatt MATH
  7. M. Tsuzuki, “Real Shintani functions on U(n,1),” Journal of Mathematical Sciences The University of Tokyo, vol. 8, no. 4, pp. 609–688, 2001. View at Google Scholar · View at Zentralblatt MATH
  8. T. Moriyama, “Spherical functions with respect to the semisimple symmetric pair (Sp(2,R),SL(2, R)×SL(2,R)),” Journal of Mathematical Sciences The University of Tokyo, vol. 6, no. 1, pp. 127–179, 1999. View at Google Scholar · View at Zentralblatt MATH
  9. T. Moriyama, “Spherical functions for the semisimple symmetry pair (Sp(2,R),SL(2,C)),” Canadian Journal of Mathematics, vol. 54, no. 4, pp. 828–865, 2002. View at Publisher · View at Google Scholar
  10. M. Tsuzuki, “Real Shintani functions on U(n,1). II. Computation of zeta integrals,” Journal of Mathematical Sciences The University of Tokyo, vol. 8, no. 4, pp. 689–719, 2001. View at Google Scholar
  11. H. Manabe, T. Ishii, and T. Oda, “Principal series Whittaker functions on SL(3,R),” Japanese Journal of Mathematics. New Series, vol. 30, no. 1, pp. 183–226, 2004. View at Google Scholar · View at Zentralblatt MATH
  12. M. Flensted-Jensen, “Spherical functions of a real semisimple Lie group. A method of reduction to the complex case,” Journal of Functional Analysis, vol. 30, no. 1, pp. 106–146, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. Howe and T. Umeda, “The Capelli identity, the double commutant theorem, and multiplicity-free actions,” Mathematische Annalen, vol. 290, no. 3, pp. 565–619, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet