Differential Galois Theory of Linear Difference Equations

2008/01/09 by Charlotte Hardouin, Hardouin, Charlotte, Michael F. Singer +1 · 2 citations
Computer Science · Engineering · #12H05 #12H10 #33B15 #39A10 #39A15 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Cryptography and Residue Arithmetic #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0801.1493

openalex publication_date 2008/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Hoelder'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 functions.

Citations

• Parameterized Telescoping Proves Algebraic Independence of Sums

Cited by

• Dimension Polynomials for Affine Partial Difference Algebraic Groups
• The Carlitz module and a differential Ax-Lindemann-Weierstrass theorem for the Euler gamma function

Related

• Descent for differential Galois theory of difference equations. Confluence and q-dependency
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