2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112631In this paper a special class of local zeta functions is studied. The main theorem states that the functions have all zeros on the line Re (s)=1/2. This is a natural generalization of the result of Bump and Ng stating that the zeros of the Mellin transform of Hermite functions have Re (s)=1/2.Number Theory11M41text