The Brylinski beta function of a coaxial layer

Abstract

In (Differential Geom. Appl. 92: Paper No. 102078, 12 pp., 2024), an analogue of Brylinski’s knot beta function was defined for a compactly supported (Schwartz) distribution T on Euclidean space. Here we consider the Brylinski beta function of the distribution defined by a coaxial layer on a submanifold of Euclidean space. We prove that it has an analytic continuation to the whole complex plane as a meromorphic function with only simple poles, and in the case of a coaxial layer on a space curve, we compute some of the residues in terms of the curvature and torsion.