数学D -模的Mellin变换的形式平稳相位

IF 1.1 2区数学 Q1 MATHEMATICS

Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-10-10 DOI:10.4171/prims/59-3-2

Ricardo García López

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引用次数: 0

摘要

给定一个完整的$\mathbb{C}\[z,z^{-1}]\langle \partial\_z\rangle$ -模块$\mathbb{M}$，遵循Loeser和Sabbah(注释)。数学。救命。$\mathbf{66}$(1991)， 458-503)，我们可以考虑它的Mellin变换，它是$\mathbb{C}$上仿射线上的一个差分系统。在这篇笔记中，我们证明了一个定相公式，该公式表明它在无穷远处的形式行为是由其奇点处由$\mathbb{M}$定义的局部细菌决定的。

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Formal Stationary Phase for the Mellin Transform of a $\mathcal D$-Module

Given a holonomic $\mathbb{C}\[z,z^{-1}]\langle \partial\_z\rangle$-module $\mathbb{M}$, following Loeser and Sabbah (Comment. Math. Helv. $\mathbf{66}$ (1991), 458–503), one can consider its Mellin transform, which is a difference system on the affine line over $\mathbb{C}$. In this note we prove a stationary phase formula, which shows that its formal behavior at infinity is determined by the local germs defined by $\mathbb{M}$ at its singular points.

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来源期刊

Publications of the Research Institute for Mathematical Sciences 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The aim of the Publications of the Research Institute for Mathematical Sciences (PRIMS) is to publish original research papers in the mathematical sciences.