Iterative q difference Galois Theory (2009)
We propose in this paper a Galois theory of $q$-difference equations where q is a root of unity. This theory is the q difference analogue of the Galois theory of iterative differential equations,...
Computation of the Galois groups occuring in M. Papanikolas's study of Carlitz logarithms (2009)
In this note, we state a theorem of compution of the unipotent radical of the Galois group of an object $U$ of a tannakian category defined over a field of positive characteristic, extension of the...
Universität Heidelberg IWR INF 368 (2008)
Zoé Chatzidakis, Charlotte Hardouin, Michael F. Singer
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable...
Differential Galois Theory of Linear Difference Equations (2008)
Hardouin, Charlotte, Singer, Michael F.
We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hoelder's Theorem...
Iterative $q$-Difference Galois Theory (2008)
Initially, the Galois theory of $q$-difference equations was built for $q$ unequal to a root of unity. This choice was made in order to avoid the increase of the field of constants to a...
On the Definitions of Difference Galois Groups (2007)
Chatzidakis, Zoé, Hardouin, Charlotte, Singer, Michael F.
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable...
Hypertranscendance et Groupes de Galois aux differences (2006)
This paper deals with criteria of algebraic independence for the derivatives of solutions of rank one difference equations. The key idea consists in deriving from the commutativity of the...