2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143581We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, and congruences for the rank differences as well as $q$-series identities of the mock theta type.9 pagesNumber TheoryCombinatoricstext