2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115103We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z = 1 case is an identity for the generating function for p-cores due to Klyachko [12] and Garvan, Kim and Stanton [7].8 pagesNumber TheoryCombinatorics11F20 (Primary), 11F27, 11F30, 05A19, 05A30, 11B65 (Secondary)text