76 citations · 382 across the 37 of their papers we have counts for
10 papers · 1 filter
Mahler equations and rationality
Reinhard Schäfke, Michael F. Singer
We give another proof of a result of Adamczewski and Bell concerning Mahler equations: A formal power series satisfying a and a Mahler equation over with…
Consistent systems of linear differential and difference equations
Reinhard Schäfke, Michael F. Singer
We consider systems of linear differential and difference equations \begin{eqnarray*} \partial Y(x) =A(x)Y(x), σY(x) =B(x)Y(x) \end{eqnarray*} with , a…
Linear Algebraic Groups as Parameterized Picard-Vessiot Galois Groups
Michael F Singer
We show that a linear algebraic group is the Galois group of a parameterized Picard-Vessiot extension of k(x), x' = 1, for certain differential fields k, if and only if its identit…
Monodromy groups of parameterized linear differential equations with regular singularities
Claude Mitschi, Michael F. Singer
We study the notion of regular singularities for parameterized complex ordinary linear differential systems, prove an analogue of the Schlesinger theorem for systems with regular s…
A Jordan-Hoelder Theorem for Differential Algebraic Groups
Phyllis J. Cassidy, Michael F. Singer
We show that a differential algebraic group can be filtered by a finite subnormal series of differential algebraic groups such that successive quotients are almost simple, that is…
Projective Isomonodromy and Galois Groups
Claude Mitschi, Michael F. Singer
In this article we introduce the notion of projective isomonodromy, which is a special type of monodromy evolving deformation of linear differential equations, based on the example…