An algorithm to recognize regular singular Mahler systems

Colin Faverjon (1) , Marina Poulet (1)

1 ICJ - Institut Camille Jordan

This paper is devoted to the study of the analytic properties of Mahler systems at 0. We give an effective characterisation of Mahler systems that are regular singular at 0, that is, systems which are equivalent to constant ones. Similar characterisations already exist for differential and (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. In particular, it gives an effective characterisation of Mahler systems to which an analog of Schlesinger’s density theorem applies.

Domaines: Théorie des nombres [math.NT]; Calcul formel [cs.SC]

Colin Faverjon, Marina Poulet. An algorithm to recognize regular singular Mahler systems. Mathematics of Computation, 2022, 91. ⟨hal-03147365v1⟩