Tohoku Mathematical Journal
2003
March
SECOND SERIES VOL. 55, NO. 1

Tohoku Math. J.
55 (2003), 1-64

Title WHITTAKER-SHINTANI FUNCTIONS FOR ORTHOGONAL GROUPS

Author Shin-ichi Kato, Atsushi Murase and Takashi Sugano

(Received November 30, 2000, revised December 25, 2001)
Abstract. As generalizations of zonal spherical functions and Whittaker functions, certain special functions on $p$-adic orthogonal groups closely related to automorphic forms are introduced. Their multiplicity one property and explicit formula are established.

2000 Mathematics Subject Classification. Primary 22E50; Secondary 11F70, 20G25, 22E35.
Key words and phrases. Spherical function, Whittaker function, orthogonal group, unramified principal series representation.

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