On the computation of the difference Galois groups of order three equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914131283542016 |
|---|---|
| author | Dreyfus, Thomas Poulet, Marina |
| author_facet | Dreyfus, Thomas Poulet, Marina |
| contents | In this paper we consider the problem of computing the difference Galois groups of order three equations for a large class of difference operators including the shift operator (Case S), the $q$-difference operator (Case Q), the Mahler operator (Case M) and the elliptic case (Case E). We show that the general problem can be reduced to several ancillary problems. We prove criteria to detect the irreducible and imprimitive Galois groups. Finally, we give a sufficient condition of differential transcendence of solutions of order three difference equations. We also compute the difference Galois group of an equation suggested by Wadim Zudilin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13448 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the computation of the difference Galois groups of order three equations Dreyfus, Thomas Poulet, Marina Number Theory Commutative Algebra 39A06, 12H05 In this paper we consider the problem of computing the difference Galois groups of order three equations for a large class of difference operators including the shift operator (Case S), the $q$-difference operator (Case Q), the Mahler operator (Case M) and the elliptic case (Case E). We show that the general problem can be reduced to several ancillary problems. We prove criteria to detect the irreducible and imprimitive Galois groups. Finally, we give a sufficient condition of differential transcendence of solutions of order three difference equations. We also compute the difference Galois group of an equation suggested by Wadim Zudilin. |
| title | On the computation of the difference Galois groups of order three equations |
| topic | Number Theory Commutative Algebra 39A06, 12H05 |
| url | https://arxiv.org/abs/2208.13448 |