Abstract
We define Eisenstein series on rank 2 hyperbolic Kac–Moody groups over \(\mathbb {R}\), induced from quasi–characters. We prove convergence of the constant term and hence the almost everywhere convergence of the Eisenstein series. We define and calculate the degenerate Fourier coefficients. We also consider Eisenstein series induced from cusp forms and show that these are entire functions.
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Notes
In an earlier version of this paper, an exponential decay in [21] was used. It was pointed out by Steve D. Miller that the rapid decay was enough to obtain our result.
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We thank the referee for many valuable comments.
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L. Carbone: This work was supported in part by NSF Grant #DMS–1101282. K.-H. Lee: This work was partially supported by a Grant from the Simons Foundation (#318706). D. Liu This work was partially supported by NSFC #11201384.
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Carbone, L., Lee, KH. & Liu, D. Eisenstein series on rank 2 hyperbolic Kac–Moody groups. Math. Ann. 367, 1173–1197 (2017). https://doi.org/10.1007/s00208-016-1428-8
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DOI: https://doi.org/10.1007/s00208-016-1428-8