Eisenstein series on loop groups
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Abstract:
Based on Garland’s work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms and prove their absolute and uniform convergence under the affine analog of Godement’s criterion. For the case of quasi-characters the resulting formula is an affine Gindikin-Karpelevich formula. Then we prove the convergence of Eisenstein series themselves in certain analogs of Siegel subsets.References
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Additional Information
- Dongwen Liu
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- MR Author ID: 913163
- Email: dongwen.liu@uconn.edu
- Received by editor(s): April 19, 2012
- Received by editor(s) in revised form: May 29, 2013
- Published electronically: September 5, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 2079-2135
- MSC (2010): Primary 22E55; Secondary 22E65, 22E67
- DOI: https://doi.org/10.1090/S0002-9947-2014-06220-X
- MathSciNet review: 3286509