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

Shintani Functions on 𝑆 𝐿 ( 3 , 𝐑 )

Keiju Sono

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.

Abstract

We investigate the Shintani functions attached to the spherical and nonspherical principal series representations of 𝑆 𝐿 ( 3 , 𝐑 ) . We give the explicit formulas of the radial part of Shintani functions and evaluate the dimension of the space of Shintani functions.