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Differential Galois theory of linear difference equations

An Erratum to this article was published on 28 July 2010

Abstract

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.

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Correspondence to Michael F. Singer.

Additional information

This material is based upon work supported by the National Science Foundation under Grant No. CCF-0634123.

An erratum to this article is available at http://dx.doi.org/10.1007/s00208-010-0551-1.

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Hardouin, C., Singer, M.F. Differential Galois theory of linear difference equations. Math. Ann. 342, 333–377 (2008). https://doi.org/10.1007/s00208-008-0238-z

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Keywords

  • Difference Equation
  • Algebraic Group
  • Galois Group
  • Galois Theory
  • Differential Dimension