Galois Groups of Difference Equations of Order Two on Elliptic Curves

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 trans...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2015
Автори: Dreyfus, T., Roques, J.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2015
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/146865
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Dreyfus, T.
Roques, J.
author_facet Dreyfus, T.
Roques, J.
citation_txt 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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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).
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2025-12-07T16:27:02Z
publishDate 2015
publisher Інститут математики НАН України
record_format dspace
spelling Dreyfus, T.
Roques, J.
2019-02-11T18:08:38Z
2019-02-11T18:08:38Z
2015
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.
1815-0659
2010 Mathematics Subject Classification: 39A06; 12H10
DOI:10.3842/SIGMA.2015.003
https://nasplib.isofts.kiev.ua/handle/123456789/146865
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).
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).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Galois Groups of Difference Equations of Order Two on Elliptic Curves
Article
published earlier
spellingShingle Galois Groups of Difference Equations of Order Two on Elliptic Curves
Dreyfus, T.
Roques, J.
title Galois Groups of Difference Equations of Order Two on Elliptic Curves
title_full Galois Groups of Difference Equations of Order Two on Elliptic Curves
title_fullStr Galois Groups of Difference Equations of Order Two on Elliptic Curves
title_full_unstemmed Galois Groups of Difference Equations of Order Two on Elliptic Curves
title_short Galois Groups of Difference Equations of Order Two on Elliptic Curves
title_sort galois groups of difference equations of order two on elliptic curves
url https://nasplib.isofts.kiev.ua/handle/123456789/146865
work_keys_str_mv AT dreyfust galoisgroupsofdifferenceequationsofordertwoonellipticcurves
AT roquesj galoisgroupsofdifferenceequationsofordertwoonellipticcurves