  We extend a formula for 1-loop black hole determinants by Denef, Hartnoll,
and Sachdev (DHS) to spinning fields on any $(d+1)$-dimensional static
spherically symmetric black hole. By carefully analyzing the regularity
condition imposed on the Euclidean eigenfunctions, we reveal an unambiguous
bulk-edge split in the 1-loop Euclidean partition function for tensor fields of
arbitrary integer spin: the bulk part captures the "renormalized" thermal
canonical partition function recently discussed in arXiv:2207.07024; the edge
part is related to quasinormal modes (QNMs) that fail to analytically continue
to a subset of Euclidean modes with enhanced fall-offs near the origin. Since
the edge part takes the form of a path integral on $S^{d-1}$, this suggests
that these are associated with degrees of freedom living on the bifurcation
surface in the Lorentzian two-sided black hole geometry. For massive higher
spin on static BTZ and massive vector on Nariai black holes, we find that the
edge partition function is related to the QNMs with lowest overtone numbers.
