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We consider the one-loop partition function for Euclidean BTZ black holebackgrounds or equivalently thermal AdS_3 backgrounds which are quotients ofH_3 (Euclidean AdS_3). The one-loop partition function is modular invariant andwe can read off the spectrum which is consistent to that found inhep-th/0001053. We see long strings and discrete states in agreement with theexpectations.Comment: 23 pages, 3 figure

Strings in AdS3 and the SL(2,R) WZW model. II: Euclidean black hole