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Eisenstein Series for Reductive Groups Over Global Function Fields II: The General Case

Published online by Cambridge University Press:  20 November 2018

L. E. Morris
L. E. Morris*
Affiliation:
Clark University, Worcester, Massachusetts
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This paper is a continuation of [5]. As stated there, the problem is to explicitly decompose the space L2 = L2(G(F)\G(A)) into simpler invariant subspaces, and to deal with the associated continuous spectrum in case G is a connected reductive algebraic group defined over a global function field. In that paper the solution was begun by studying Eisenstein series associated to cusp forms on Levi components of parabolic subgroups; these Eisenstein series and the associated intertwining operators were shown to be rational functions satisfying functional equations. To go further it is necessary to consider more general Eisenstein series and intertwining operators, and to show that they have similar properties. Such Eisenstein series arise from the cuspidal ones by a residue taking process, which is detailed in a disguised form suitable for induction in the first part of this paper: the main result is a preliminary form of the spectral decomposition.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 5 , 01 October 1982 , pp. 1112 - 1182
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Arthur, J. G., Eisenstein series and the trace formula, Proc. Symp. Pure Math. 33, part I (Amer. Math. Soc., Providence, R. I., 1979), 253–274./Google Scholar
2. Borel, A. and Jacquet, H., Automorphic forms and automorphic representations, ibid., 189–202./Google Scholar
3. Langlands, R. P., On the functional equations satisfied by Eisenstein series, Springer Lecture Notes 54 (1976)./Google Scholar
4. Langlands, R. P., On the notion of an automorphic representation, Proc. Symp. Pure Math. 33, part I (Amer. Math. Soc, Providence, R. I., 1979), 203–207./Google Scholar
5. Morris, L. E., Eisenstein series for reductive groups over global function fields I: the cusp form case, Can. J. Math.Google Scholar
6. Morris, L. E., Square integrable automorphic forms, to appear.Google Scholar
7. Osborne, M. S. and Warner, G., Towards the trace formula in the sense of Selberg, notes to appear under the title The theory of Eisenstein systems in the Pure and Applied Mathematics series of monographs of Academic Press.Google Scholar