2020/12/22 by Ehud de Shalit, de Shalit, Ehud, José M. Gutiérrez +1
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2012.12353
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.