Rigid irregular connections on P^1

TL;DR

This paper extends Katz's middle convolution algorithm by incorporating Fourier transform, enabling the description of rigid connections on the projective line with arbitrary singularities.

Contribution

The paper introduces an extended algorithm combining middle convolution and Fourier transform to analyze rigid connections with irregular singularities.

Findings

Extended algorithm describes rigid connections with arbitrary singularities.

Fourier transform integration enhances the analysis of irregular singularities.

Provides a new tool for studying complex differential equations on P^1.

Abstract

N.Katz's middle convolution algorithm provides a description of rigid connections on the projective line with regular singularities. We extend the algorithm by adding the Fourier transform to it. The extended algorithm provides a description of rigid connections with arbitrary singularities.