19 citations · 41 across the 7 of their papers we have counts for
6 papers · 1 filter
The q-analogue of the wild fundamental group and the inverse problem of the Galois theory of q-difference equations
Jean-Pierre Ramis, Jacques Sauloy
In previous papers, we defined -analogues of alien derivations for linear analytic -difference equations with integral slopes and proved a density theorem (in the Galois grou…
Local analytic classification of q-difference equations
J. -P. Ramis, J. Sauloy, C. Zhang
We essentially achieve Birkhoff's program for q-difference equations by giving three different descriptions of the moduli space of isoformal analytic classes. This involves an exte…
The q-analogue of the wild fundamental group (II)
J. -P. Ramis, J. Sauloy
In [RS1], we defined q-analogues of alien derivations and stated their basic properties. In this paper, we prove the density theorem and the freeness theorem announced in loc. cit.…
The q-analogue of the wild fundamental group (I)
J. -P. Ramis, J. Sauloy
We describe an explicit construction of galoisian Stokes operators for irregular linear q-difference equations. These operators are parameterized by the points of an elliptic curve…
Algebraic construction of the Stokes sheaf for irregular linear q-difference equations
Jacques Sauloy
The local analytic classification of irregular linear q-difference equations has recently been obtained by J.-P. Ramis, J. Sauloy and C. Zhang. Their description involves a q-analo…
Galois theory of fuchsian q-difference equations
Jacques Sauloy
We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the…