论文标题
关于某些$γ$ - 差异模块的结构
On the structure of certain $Γ$-difference modules
论文作者
论文摘要
这是一份很大程度上的说明文件，在[SCH-SI1，SCH-SI2]的结果中提供了一个独立的帐户，在该案例中表示为2q和2m。 Schäfke和Singer的这些论文为[Bez-Bou，ad-Be]的主要定理提供了新的证据，内容符合功率系列的合理性，使一对独立的Q-Difference或Mahler方程式满足。 我们强调$γ$ - 差异模块的语言，而不是差方程或系统。尽管在上面提到的两种情况下，这只是一种语义变化，但我们也将新案例视为1M1Q。在这里，组$γ$是概括性的二面而不是Abelian，方程式语言不足。 在最后一部分中，我们解释了如何在情况2Q中概括主要定理以获取有限特征。
This is a largely expository paper, providing a self-contained account on the results of [Sch-Si1, Sch-Si2], in the cases denoted there 2Q and 2M. These papers of Schäfke and Singer supplied new proofs to the main theorems of [Bez-Bou, Ad-Be], on the rationality of power series satisfying a pair of independent q-difference, or Mahler, equations. We emphasize the language of $Γ$-difference modules, instead of difference equations or systems. Although in the two cases mentioned above this is only a semantic change, we also treat a new case, which may be labeled 1M1Q. Here the group $Γ$ is generalized dihedral rather than abelian, and the language of equations is inadequate. In the last section we explain how to generalize the main theorems in case 2Q to finite characteristic.
