English

On the Mellin transform of a D-module

Algebraic Geometry 2021-01-11 v3

Abstract

Given a holonomic D-module M on a 1-dimensional torus, one can consider its Mellin transform, which is a difference system on the affine line. In this note we prove a formal stationary phase formula, which shows that the formal behavior at infinity of the Mellin transform of M is determined by the local germs defined by M at its singular points.

Cite

@article{arxiv.1804.09776,
  title  = {On the Mellin transform of a D-module},
  author = {Ricardo Garcia Lopez},
  journal= {arXiv preprint arXiv:1804.09776},
  year   = {2021}
}

Comments

A mistake pointed up by C. Sabbah has been corrected, exposition improved

R2 v1 2026-06-23T01:36:01.809Z