CR invariants of weight five in the Bergman kernel
This article continues the development of Fefferman's program [\textit{Ch. Fefferman}, Adv. Math. 31, 131-262 (1979; Zbl 0444.32013)] to express the asymptotic expansion of the Bergman kernel function on the diagonal near the boundary of a strongly pseudoconvex domain in \(\mathbf{C}^n\) in terms of CR invariants of the boundary. The authors also study the Szegő kernel function. The paper refines earlier results of \textit{C. R. Graham} [Lect. Notes Math. 1276, 108-135 (1987; Zbl 0626.32027)] and the authors [Komatsu, Gen (ed.) et al., Lect. Notes Pure Appl. Math. 143, 77-96 (1993; Zbl 0793.32009)] by identifying the coefficients in the expansion through the invariants of weight \(\leq 5\) when the dimension \(n=2\). For further advances on the singularity of the Bergman kernel function in \(\mathbf{C}^n\), see a paper of the first author [Construction of boundary invariants and the logarithmic singularity in the Bergman kernel, Ann. Math., to appear].
scientific article; zbMATH DE number 1295248
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