Subtlety of oscillation indices of oscillatory integrals of real analytic functions
Complex Variables
2026-01-21 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2511.16257,
title = {Subtlety of oscillation indices of oscillatory integrals of real analytic functions},
author = {In-Kyun Kim and Morihiko Saito},
journal= {arXiv preprint arXiv:2511.16257},
year = {2026}
}