Spectrum of a linear differential equation over a field of formal power series

Tinhinane A. Azzouz

doi:10.1016/j.jnt.2020.11.021

paper

Spectrum of a linear differential equation over a field of formal power series

arXiv:1808.02382 · doi:10.1016/j.jnt.2020.11.021

Abstract

In this paper we associate to a linear differential equation with coefficients in the field of Laurent formal power series a new geometric object, a spectrum in the sense of Berkovich. We will compute this spectrum and show that it contains interesting informations about the equation.