Asymptotic expansion of the off-diagonal Bergman kernel on compact K\"ahler manifolds

We compute the first four coefficients of the asymptotic off-diagonal expansion of the Bergman kernel for the N-th power of a positive line bundle on a compact Kaehler manifold, and we show that the coefficient b_1 of the N^{-1/2} term vanishes when we use a K-frame. We also show that all the coefficients of the expansion are polynomials in the K-coordinates and the covariant derivatives of the curvature and are homogeneous with respect to the weight w.