Newton polyhedra and the Bergman kernel

The purpose of this paper is to study singularities of the Bergman kernel at the boundary for pseudoconvex domains of finite type from the viewpoint of the theory of singularities. Under some assumptions on a domain Omega in <copf>(n+1), the Bergman kernel B(z) of Omega takes the form near a boundary point p: [GRPAHICS] where (w,rho) is some polar coordinates on a nontangential cone Lambda with apex at p and rho means the distance from the boundary. Here Phi admits some asymptotic expansion with respect to the variables rho(1/m) and log(1/rho) as rho-->0 on Lambda. The values of d(F)>0, m(F)is an element of<zopf>(+) and mis an element of are determined by geometrical properties of the Newton polyhedron of defining functions of domains and the limit of Phi as rho-->0 on Lambda is a positive constant depending only on the Newton principal part of the defining function. Analogous results are obtained in the case of the Szego kernel.