An algorithm to recognize regular singular Mahler systems

Faverjon, Colin; Poulet, Marina

doi:10.1090/mcom/3758

An algorithm to recognize regular singular Mahler systems
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by Colin Faverjon and Marina Poulet;

Math. Comp. 91 (2022), 2905-2928

DOI: https://doi.org/10.1090/mcom/3758

Published electronically: August 1, 2022

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Abstract:

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.

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