AdS one-loop partition functions from bulk and edge characters

We show that the one-loop partition function of any higher spin field in $(d+1)$-dimensional Anti-de Sitter spacetime can be expressed as an integral transform $\text{SO}(2,d)$ bulk character and $\text{SO}(2,d-2)$ edge character. apply this formula to various higher-spin Vasiliev gravities find miraculous (almost) cancellations between characters lead agreement with predictions HS/CFT holography. also discuss about relation representation Rindler-AdS thermal function.