Differential Galois theory of linear difference equations

By Charlotte Hardouin, Michael F. Singer. 2008

150 citations recorded by the source corpus.

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 Hölder’s theorem that the Gamma function satisfies no polynomial differential equation and are able to give general results that imply, for example, that no differential relationship holds among solutions of certain classes of q-hypergeometric equations.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9690f694974ce8f0b6a1ad7bce7500d256902018

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Alexey Ovchinnikov
2. S. Gorchinskiy
3. H. Gillet

In Geometry and Topology

1. Alexey Ovchinnikov
2. S. Gorchinskiy
3. H. Gillet

Citations in the corpus

• Parameterized Picard-Vessiot extensions and Atiyah extensions (2011, methodology): “Differential algebraic dependencies among solutions of difference equations were studied in [31, 32, 33, 18, 20, 19, 21, 17, 16, 26].”