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This article is cited in 6 scientific papers (total in 6 papers)
Galois Groups of Difference Equations of Order Two on Elliptic Curves
Thomas Dreyfusa, Julien Roquesb a Université Paul Sabatier, Institut de Mathématiques de Toulouse, 18 route de Narbonne, 31062 Toulouse, France
b Institut Fourier, Université Grenoble 1, CNRS UMR 5582, 100 rue des Maths, BP 74, 38402 St Martin d’Hères, France
Abstract:
This paper is concerned with difference equations on elliptic curves. We establish some general properties of the difference Galois groups of equations of order two, and give applications to the calculation of some difference Galois groups. For instance, our results combined with a result from transcendence theory due to Schneider allow us to identify a large class of discrete Lamé equations with difference Galois group $\operatorname{GL}_{2}(\mathbb C)$.
Keywords:
linear difference equations; difference Galois theory; elliptic curves.
Received: August 6, 2014; in final form January 8, 2015; Published online January 13, 2015
Citation:
Thomas Dreyfus, Julien Roques, “Galois Groups of Difference Equations of Order Two on Elliptic Curves”, SIGMA, 11 (2015), 003, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma984 https://www.mathnet.ru/eng/sigma/v11/p3
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Abstract page: | 358 | Full-text PDF : | 30 | References: | 23 |
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