Subtlety of oscillation indices of oscillatory integrals of real analytic functions (2511.16257v1)

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 where the number of variables is even and smaller than the degree.