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Hypertranscendance des systèmes aux différences diagonaux

Part of: Differential equations in the complex domain Difference and functional equations Difference equations Differential and difference algebra

Published online by Cambridge University Press:  01 May 2008

Charlotte Hardouin
Charlotte Hardouin*
Affiliation:
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany (email: [email protected])
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Abstract

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This paper deals with criteria of algebraic independence for the derivatives of solutions of diagonal difference systems. The key idea consists in deriving from the commutativity of the differentiation and difference operators a sequence of iterated extensions of the original difference module, thereby setting the problem in the framework of difference Galois theory and finally reducing it to an exercise in linear algebra on the group of divisors of the involved elliptic curve or torus.

Keywords

linear difference equationsdifference Galois groupstannakian categoryhypertranscendence

MSC classification

Secondary: 12H10: Difference algebra 12H05: Differential algebra 34M15: Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) 39A13: Difference equations, scaling ($q$-differences)
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 3 , May 2008 , pp. 565 - 581
Copyright
Copyright © Foundation Compositio Mathematica 2008