2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213362We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields over $\mathbb{Q}(\sqrt{-m})$ for all m. For each imaginary quadratic field $\mathbb{Q}(\sqrt{-m})$, we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13,14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger's fifteen theorem and ours is the number 13.20 PagesNumber Theory11E39 (Primary); 11E20, 11E41 (Secondary)text