An algorithm computing non solvable spectral radii of $p$-adic differential equations

TL;DR

This paper presents an explicit algorithm to compute the non solvable spectral radii of convergence for solutions of differential modules over certain points in the Berkovich affine line, advancing understanding in p-adic differential equations.

Contribution

It introduces a novel algorithm specifically designed for calculating non solvable spectral radii in p-adic differential equations over Berkovich points.

Findings

Algorithm explicitly computes non solvable spectral radii

Applicable to points of type 2, 3, or 4 in Berkovich line

Enhances computational tools for p-adic differential equations

Abstract

We obtain an algorithm computing explicitly the values of the non solvable spectral radii of convergence of the solutions of a differential module over a point of type 2, 3 or 4 of the Berkovich affine line.