This nine-chapter monograph introduces a rigorous investigation of q-difference operators in
standard and fractional settings. It starts with elementary calculus of q-differences and …

Now in its second edition, this volume provides a uniquely detailed study of $ P $-adic
differential equations. Assuming only a graduate-level background in number theory, the text …

Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-
adic theories, geometry of numbers…. These functorial filtrations, which are indexed by …

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 extension of …

After introducing q-analogs of the Borel and Laplace transformations, we prove that to every
formal power series solution of a linear q-difference equation with rational coefficients, we …

An interesting theme in complex differential geometry is to find a correspondence between
algebraic objects and differential geometric objects. One of the most attractive is the non …

We prove an ultrametric $ q $-difference version of the Maillet-Malgrange theorem on the
Gevrey nature of formal solutions of nonlinear analytic $ q $-difference equations. Since …

In this paper, we consider a q-analogue of the Borel-Laplace summation where q> 1 is a
real parameter. In particular, we show that the Borel-Laplace summation of a divergent …

The local analytic classification and the description of the Galois group for complex linear
analytic q-difference equations have been obtained by Ramis, Sauloy and Zhang [15, 14] …

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 extension of …