Refinements to the Kuznetsov Formula for Laplace-Beltrami Operators

Wyman and Xi (2023) proved a Kuznetsov-type theorem for the submanifold counting function associated with Laplace–Beltrami eigenvalues. We refine the results of Wyman and Xi, improving their asymptotic: we remove a constant in the codimension-one case, and we prove a new asymptotic in the case that the set of looping times has measure zero.