# Descent for differential Galois theory of difference equations: confluence and q-dependence

@article{Vizio2011DescentFD, title={Descent for differential Galois theory of difference equations: confluence and q-dependence}, author={L. Vizio and C. Hardouin}, journal={Pacific Journal of Mathematics}, year={2011}, volume={256}, pages={79-104} }

The present paper contains two results that generalize and improve constructions of Hardouin and Singer. In the case of a derivation, we prove that the parametrized Galois theory for difference equations constructed by Hardouin and Singer can be descended from a differentially closed to an algebraically closed field. In the second part of the paper, we show that the theory can be applied to deformations of q-series to study the differential dependence with respect to x d d x and q d dq . We… CONTINUE READING

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