Correlation functions of one unit spectral flowed states in string theory on AdS_3 are considered. We present the modified Knizhnik-Zamolodchikov and null vector equations to be satisfied by amplitudes containing states in winding sector one and study their solution corresponding to the four point function including one w=1 field. We compute the three point function involving two one unit spectral flowed operators and find expressions for amplitudes of three w=1 states satisfying certain

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... lar relations among the spins of the fields. Several consistency checks are performed.