19 citations · 41 across the 7 of their papers we have counts for
9 papers
Geometry of the space of monodromy data
Jean-Pierre Ramis, Jacques Sauloy
In a paper published by the Annales de la Faculté de Sciences de Toulouse, with Yousuke Ohyama, we defined and studied a space of monodromy data underlying the well known derivatio…
On the vanishing of coefficients of the powers of a theta function
Jacques Sauloy, Changgui Zhang
A result on the Galois theory of -difference equations \cite{JSTALPAEN} leads to the following question: if $q \in \Cs$, $\lmod q \rmod < 1$ and if one sets $\thq(z) := \sum\lim…
The space of monodromy data for the Jimbo-Sakai family of -difference equations
Yousuke Ohyama, Jean-Pierre Ramis, Jacques Sauloy
We formulate a geometric Riemann-Hilbert correspondence that applies to the derivation by Jimbo and Sakai of equation -PVI from ``isomonodromy'' conditions. This is a step withi…
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.…