q-Deformation of Meromorphic Solutions of Linear Differential Equations
Abstract
In this paper, we consider the behaviour, when goes to , of the set of a convenient basis of meromorphic solutions of a family of linear -difference equations. In particular, we show that, under convenient assumptions, such basis of meromorphic solutions converges, when goes to , to a basis of meromorphic solutions of a linear differential equation. We also explain that given a linear differential equation of order at least two, which has a Newton polygon that has only slopes of multiplicities one, and a basis of meromorphic solutions, we may build a family of linear -difference equations that discretizes the linear differential equation, such that a convenient family of basis of meromorphic solutions is a -deformation of the given basis of meromorphic solutions of the linear differential equation.
Keywords
Cite
@article{arxiv.1501.02992,
title = {q-Deformation of Meromorphic Solutions of Linear Differential Equations},
author = {Thomas Dreyfus},
journal= {arXiv preprint arXiv:1501.02992},
year = {2019}
}