2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71968Here we characterise in a complete and explicit way the relations of algebraic dependence over $\QQ$ of complex values of Hecke-Mahler series taken at algebraic points of the multiplicative group $\GG_m^2(\CC)$. Our result contains previous theorems by Loxton and van der Poorten, Mahler, and Masser.Number Theory11J85text