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S at a Split Place Matching Integrals of Spherical Functions Spherical Matching in the Split Case Applications to Cyclic Representations Local Cyclic Representations Appendix. Multiplicity one theorems 1. Statement of Results. Let C be an algebraic subgroup of an algebraic group G over a global eld F , and denote by : G(F )nG(A ) ! C a cusp form in the cuspidal representation of the adele group G(A ), where A is the ring of F -adeles. Denote by Z the center of G and by ! ! : Z(A ) Z (F ).

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