A note on a refined version of Anderson–Brownawell–Papanikolas criterion

We give a refinement of the linear independence criterion over function fields developed by Anderson, Brownawell and Papanikolas [Greg W. Anderson, W. Dale Brownawell, Matthew A. Papanikolas, Determination of the algebraic relations among special Γ-values in positive characteristic, Ann. of Math. 160 (2004) 237–313]. As a consequence, a function field analogue of the Siegel–Shidlovskii theorem is derived.