{"paper":{"title":"The second coefficient of the asymptotic expansion of the weighted Bergman kernel for $(0,q)$ forms on $\\Complex^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Chin-Yu Hsiao","submitted_at":"2012-08-19T09:21:19Z","abstract_excerpt":"Let $\\phi\\in C^\\infty(\\Complex^n)$ be a given real valued function. We assume that $\\pr\\ddbar\\phi$ is non-degenerate of constant signature $(n_-,n_+)$ on $\\Complex^n$. When $q=n_-$, it is well-known that the Bergman kernel for $(0,q)$ forms with respect to the $k$-th weight $e^{-2k\\phi}$, $k>0$, admits a full asymptotic expansion in $k$. In this paper, we compute the trace of the second coefficient of the asymptotic expansion on the diagonal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3818","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}