The Szegö kernel for non-pseudoconvex tube domains in C²

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We consider the Szegö kernel for non-pseudoconvex domains in C² given by Ω= (z,w): Im w > b(Re z) for b a non-convex even-degree polynomial with positive leading coefficient. This is an extension of results previously obtained by the authors for the case in which b has degree 4. We show that the Szegö kernel has singularities off the diagonal of the boundary of Ω × Ω for all such domains, as well as points on the diagonal of the boundary at which it is finite.