An algorithm to recognize regular singular Mahler systems

Abstract

This paper is devoted to the study of the analytic properties of Mahler systems at 0 0 . We give an effective characterisation of Mahler systems that are regular singular at 0 0 , that is, systems which are equivalent to constant ones. Similar characterisations already exist for differential and ( q q -)difference systems but they do not apply in the Mahler case. This work fills in the gap by giving an algorithm which decides whether or not a Mahler system is regular singular at 0 0 . In particular, it gives an effective characterisation of Mahler systems to which an analog of Schlesinger’s density theorem applies.