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Galois Groups of Difference Equations of Order Two on Elliptic Curves
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Galois Groups of Difference Equations of Order Two on Elliptic Curves
Інший ID:
2010 Mathematics Subject Classification: 39A06; 12H10
DOI:10.3842/SIGMA.2015.003
DOI:10.3842/SIGMA.2015.003
Посилання:
Galois Groups of Difference Equations of Order Two on Elliptic Curves / T. Dreyfus, J. Roques // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 35 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Algebraic Methods in Dynamical Systems. The full
collection is available at http://www.emis.de/journals/SIGMA/AMDS2014.html.
Our original interest in dif ference equations on elliptic curves arose from discussions with JeanPierre
Ramis some years ago. We thank Jean-Pierre Ramis and Michael Singer for interesting
discussions. We thank the referees for their careful reading and useful suggestions. The first
author is founded by the labex CIMI. The second author is partially funded by the French ANR
project QDIFF (ANR-2010-JCJC-010501).
Дата:
2015
Переглядів:
784
Завантажень:
262
Анотація:
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 GL₂(C).
