Many articles have recently been devoted to Mahler equations, partly because of their links with other branches of mathematics such as automata theory. Hahn series (a generalization of the Puiseux series allowing arbitrary exponents of the indeterminate as long as the set that supports them is well-ordered) play a central role in the theory of Mahler equations. In this paper, we address the following fundamental question: is there an algorithm to calculate the Hahn series solutions of a given linear Mahler equation? What makes this question interesting is the fact that the Hahn series appearing in this context can have complicated supports with infinitely many accumulation points. Our (positive) answer to the above question involves among other things the construction of a computable well-ordered receptacle for the supports of the potential Hahn series solutions.

翻译：近年来，许多文章致力于研究马勒方程，部分原因在于其与自动机理论等数学分支的紧密联系。哈恩级数（作为普伊瑟级数的推广，允许未定元具有任意指数，只要支撑这些指数的集合是良序的）在马勒方程理论中扮演着核心角色。本文探讨以下基本问题：是否存在一种算法，能够计算给定线性马勒方程的哈恩级数解？该问题的有趣之处在于，此类哈恩级数的支撑集可能具有复杂的结构，包含无穷多个聚点。我们对上述问题给出肯定回答，其论证过程涉及为潜在哈恩级数解的支撑集构造一个可计算的良序容器。