2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143718We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3. The expression also elucidates an SL(2,Z) invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as k goes to infinity.54 pages, harvmac b-mode. 9 figures; minor mistakes corrected; V3: An important mistake has been corrected. Conclusions essentially unchangedHigh Energy Physics - Theorytext