2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185462We consider the one-loop partition function for Euclidean BTZ black hole backgrounds or equivalently thermal AdS_3 backgrounds which are quotients of H_3 (Euclidean AdS_3). The one-loop partition function is modular invariant and we can read off the spectrum which is consistent to that found in hep-th/0001053. We see long strings and discrete states in agreement with the expectations.23 pages, 3 figuresHigh Energy Physics - Theorytext