Poles of \(\int_Af^s\bullet\) for an almost isolated singularity (Q1275643)

Distributions are studied arising from germs of real analytic functions. Let \(f:(\mathbb{R}^{n+1},0)\to(\mathbb{R},0)\) be the germ of a real analytic function such that the complexified germ has an almost isolated singularity at 0 for an eigenvalue \(e^{-2\pi iu}\) of the monodromy, \(u\in(0,1)\) and rational. Let \(A\) be a linear combination of the connected components of \(\mathbb{R}^{n+1} \setminus \{f=0\}\). The distribution \(\int_Af^s \bullet\) is studied and necessary and sufficient conditions are given for the property that it admits poles in \(-u+\mathbb{N}\).