One-loop divergences in two dimensions for the higher-spin fields

A simple formula for one-loop logarithmic divergences on the background of two-dimensional curved space-time is derived for the case when the second variation of the action is a non-minimal second-order operator with small non-minimal terms. In particular, this formula allows us to calculate the terms that are integrals of total derivatives. As an application of this result, the one-loop divergences for the higher-spin fields on the background with constant curvature are obtained in a non-minimal gauge, which depends on two parameters. By the explicit calculation, we demonstrate that within the considered accuracy the result is gauge independent. Moreover, this result appears to be independent of the spin.