2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220471We introduce a polynomial zeta function $ζ^{(p)}_{P_n}$, related to certain problems of mathematical physics, and compute its value and the value of its first derivative at the origin $s=0$, by means of a very simple technique. As an application, we compute the determinant of the Dirac operator on quaternionic vector spaces.7 pages, 1 figureMathematical PhysicsHigh Energy Physics - TheoryNumber Theory11M99text