An explicit stationary phase formula for the local formal Fourier-Laplace transform

TL;DR

This paper presents an explicit stationary phase formula for the local Fourier-Laplace transform of formal germs of meromorphic connections with irregular singularities, extending previous complex analogues.

Contribution

It provides a new explicit formal stationary phase formula for local Fourier-Laplace transforms of meromorphic connections with irregular singularities.

Findings

Derived an explicit formula for the local Fourier-Laplace transform

Extended complex analogue of previous formulas

Applicable to irregular singularities in meromorphic connections

Abstract

We give an explicit formula (i.e., a formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. This is a complex analogue of the formulas in the preprint math/0702436v1.