13 citations · 22 across the 4 of their papers we have counts for
4 papers
An ultrametric version of the Maillet-Malgrange theorem for nonlinear q-difference equations
Lucia Di Vizio
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 °_q and…
Continuity of the radius of convergence of p-adic differential equations on Berkovich analytic spaces
Francesco Baldassarri, Lucia Di Vizio
We consider a vector bundle with integrable connection (\cE,\na) on an analytic domain U in the generic fiber \cX_η of a smooth formal p-adic scheme \cX, in the sense of Berkovich.…
On q-summation and confluence
Lucia Di Vizio, Changgui Zhang
This paper is divided in two parts. In the first part we consider irregular singular analytic q-difference equations, with q\in ]0,1[, and we show how the Borel sum of a divergent…
Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems)
Lucia Di Vizio
Inspired by the theory of p-adic differential equations, this paper introduces an analogous theory for q-difference equations over a local field, when |q|=1. We define some basic c…