Dimensions of solution spaces of H-systems

• Autores: S. A. Abramov, M. Petkovsek
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 43, Nº 5, 2008, pág. 377
• Idioma: inglés
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• Resumen

  • An H-system is a system of first-order linear homogeneous recurrence equations for a single unknown function T, with coefficients which are polynomials with complex coefficients. We consider solutions of image-systems which are of the form image where either image, or image and S is the set of integer singularities of the system. It is shown that any natural number is the dimension of the solution space of some consistent image-system, and that in the case d?2 there are image-systems whose solution space is infinite dimensional. The relationship between dimensions of solution spaces in the two cases image and image is investigated. We prove that every consistent image-system image has a non-zero solution T with image. Finally we give an appropriate corollary to the Ore¿Sato theorem on possible forms of solutions of image-systems in this setting.