Local cubic vertex functions for three massless higher even spin fields on spaces AdS_D: An analytic approach

Local cubic vertex functions of three higher even spin fields on AdS_D are constructed from the Green function of three conserved currents that are dual to the higher spin fields. Conservation of the currents implies lowest order gauge invariance. These vertex functions appear by the UV divergence as the residue of the highest order pole in the dimensional regularization parameter \epsilon. The method works for even D and maintains covariance at any step. The resulting formula is quite concise.