2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168408In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in his book[p.189, Tata Lectures on Theta I (1983), Birkhauser].Added the detailed proof ; added 4 more references ; Removal of Remark 2.3Number Theory11F27 (Primary); 11F37, 11F50 (Secondary)text