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On the Analytic Continuation of c-Functions

Published online by Cambridge University Press:  20 November 2018

Paul F. Ringseth
Paul F. Ringseth*
Affiliation:
University of Washington, Seattle, Washington
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Let G be a reductive Lie group; Γ a nonuniform lattice in G. Then the theory of Eisenstein series plays a major role in the spectral decomposition of L2(G/Γ) (cf. [5]). One of the most difficult aspects of the subject is the analytic continuation of the Eisenstein series along with its associated c-function. This was originally done by Langlands using some very difficult analysis (cf. [5]). Later Harish-Chandra was able to simplify somewhat the most difficult part of the continuation, the continuation to zero, by the introduction of the Maas-Selberg relation. The purpose of this note is to give a simplified account of this particular part of the theory.

Our chief tool will be the truncation operator of Arthur (cf. [1] and [8]), the systematic utilization of which has the effect of streamlining the earlier accounts, especially in so far as continuation to zero is concerned, which is reduced to an elementary manipulation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 3 , 01 June 1988 , pp. 513 - 531
Copyright
Copyright © Canadian Mathematical Society 1988

References

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