On the algebraic relations between Mahler functions
On the algebraic relations between Mahler functions
复制标题
马勒函数之间的代数关系
DOI：
10.1090/tran/6945
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
J. Roques
中科院分区：
文献类型：
--
作者：
J. Roques
近年来，许多作者研究了自动序列生成列之间的代数关系。证明了这些级数是马勒型方程的解。本文主要研究Mahler型方程的差分Galois群（这些群反映了方程解之间的代数关系）。特别地，我们详细地研究了二阶方程，并计算了与Baum-Sweet和Rudin-Shapiro自动序列相关的经典方程的差分Galois群。
In the last years, a number of authors have studied the algebraic relations between the generating series of automatic sequences. It turns out that these series are solutions of Mahler type equations. This paper is mainly concerned with the difference Galois groups of Mahler type equations (these groups reflect the algebraic relations between the solutions of the equations). In particular, we study in details the equations of order 2, and compute the difference Galois groups of classical equations related to the Baum-Sweet and to the Rudin-Shapiro automatic sequences.