2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103558In a recent work, Paycha and Scott establish formulas for all the Laurent coefficients of Tr(AP^{-s}) at the possible poles. In particular, they show a formula for the zero'th coefficient at s=0, in terms of two functions generalizing, respectively, the Kontsevich-Vishik canonical trace density, and the Wodzicki-Guillemin noncommutative residue density of an associated operator. The purpose of this note is to provide a proof of that formula relying entirely on resolvent techniques (for the sake of possible generalizations to situations where powers are not an easy tool). - We also give some corrections to transition formulas used in our earlier works.Minor corrections. To appear in a proceedings volume in honor of K. Wojciechowski, "Analysis and Geometry of Boundary Value Problems", World Scientific, 19 pagesAnalysis of PDEsSpectral Theory58J42, 35S05, 58J35text