Thomas Dreyfus, Julien Roques, “Galois Groups of Difference Equations of Order Two on Elliptic Curves”, SIGMA, 2015, Volume 11,003, 23 pp.

This article is cited in 7 papers

Galois Groups of Difference Equations of Order Two on Elliptic Curves

Thomas Dreyfus^a, Julien Roques^b

^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.

MSC: 39A06; 12H10

Received: August 6, 2014; in final form January 8, 2015; Published online January 13, 2015

Language: English

DOI: 10.3842/SIGMA.2015.003