Abstract
LetG andH ⊂G be two real semisimple groups defined overQ. Assume thatH is the group of points fixed by an involution ofG. Letπ ⊂L 2(H\G) be an irreducible representation ofG and letf επ be aK-finite function. Let Γ be an arithmetic subgroup ofG. The Poincaré seriesP f(g)=ΣH∩ΓΓ f(γ{}itg) is an automorphic form on Γ\G. We show thatP f is cuspidal in some cases, whenH ∩Γ\H is compact.
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Partially supported by NSF Grant # DMS 9103608.
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Savin, G. Cusp forms. Israel J. Math. 80, 195–205 (1992). https://doi.org/10.1007/BF02808162
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DOI: https://doi.org/10.1007/BF02808162