Subtlety of oscillation indices of oscillatory integrals of real analytic functions

Fuente: arXiv
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Main Authors: Kim, In-Kyun, Saito, Morihiko
Format: Preprint
Published: 2025
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author Kim, In-Kyun
Saito, Morihiko
author_facet Kim, In-Kyun
Saito, Morihiko
contents For a locally defined real analytic function, we study the relation between the oscillation index of oscillatory integrals and the real log canonical threshold. The former is always negative, and its absolute value is greater than or equal to the latter. They coincide very often, but there are certain exceptional cases even in the Newton nondegenerate convenient homogeneous case, for instance if the number of variables is even and smaller than the degree. This does not seem compatible with some standard formula in the literature, and there must be some error somewhere, although it does not seem easy to find it inside this paper.
format Preprint
id arxiv_https___arxiv_org_abs_2511_16257
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Subtlety of oscillation indices of oscillatory integrals of real analytic functions
Kim, In-Kyun
Saito, Morihiko
Complex Variables
Algebraic Geometry
For a locally defined real analytic function, we study the relation between the oscillation index of oscillatory integrals and the real log canonical threshold. The former is always negative, and its absolute value is greater than or equal to the latter. They coincide very often, but there are certain exceptional cases even in the Newton nondegenerate convenient homogeneous case, for instance if the number of variables is even and smaller than the degree. This does not seem compatible with some standard formula in the literature, and there must be some error somewhere, although it does not seem easy to find it inside this paper.
title Subtlety of oscillation indices of oscillatory integrals of real analytic functions
topic Complex Variables
Algebraic Geometry
url https://arxiv.org/abs/2511.16257