On Baker type lower bounds for linear forms

A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers $1,{\mathrm{\Theta }}_1,\mathrm{.}\mathrm{.}\mathrm{.},{\mathrm{\Theta }}_m\in {\mathbb{C}}^{\ast }$ over the ring ${\mathbb{Z}}_{\mathbb{I}}$ of an imaginary quadratic field $\mathbb{I}$. This work deals with the simultaneous auxiliary functions case.