多变量Mahler方法I：正则奇异系统理论
Mahler's method in several variables I: The theory of regular singular systems
摘要：
这是第一部分的工作，致力于研究线性马勒系统的几个变量的角度超越和代数独立。我们证明了两个主要的结果，系统是正规奇异的原点。我们感兴趣的马勒的方法来自可能的应用这些结果涉及自动机理论的老问题，其中涉及的扩展都自然数和实数在整数基地。特别是，涉及有限自动机和基地变化的问题。这类应用研究在第二部分的这项工作。
英文摘要：
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at the origin. Our interest in Mahler's method comes from the possible applications of these results to old problems involving automata theory and which concern the expansion of both natural numbers and real numbers in integer bases. In particular, problems which involve finite automata and base change. Such applications are studied in Part II of this work.
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