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arXiv · 1009.2538

Differential equations, difference equations and algebraic relations: An extension to a theorem of Compoint

Camilo Sanabria
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Abstract

Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its Galois Group G has finite determinant group and is reductive. In this context, the ideal of algebraic relations satisfied by a full system of solutions is generated by the G-invariants it contains. This result extends a theorem of E. Compoint.

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Camilo Sanabria. 2010-09-13. Differential equations, difference equations and algebraic relations: An extension to a theorem of Compoint. https://arxiv.org/abs/1009.2538

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