On the distribution of the principal series in

Authors:
Roberto J. Miatello and Jorge A. Vargas

Journal:
Trans. Amer. Math. Soc. **279** (1983), 63-75

MSC:
Primary 22E45; Secondary 11F70, 22E40, 58G25

MathSciNet review:
704602

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Abstract: Let be a semisimple Lie group of split rank one with finite center. If is a discrete cocompact subgroup, then . For fixed , let denote the classes of irreducible unitary principal series . Let, for , where is the eigenvalue of (the Casimir element of ) on the class . In this paper, we determine the singular part of the asymptotic expansion of as if is torsion free, and the first term of the expansion for arbitrary . As a consequence, if and is without connected compact normal subgroups, then

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1983-0704602-9

Article copyright:
© Copyright 1983
American Mathematical Society