{"paper":{"title":"The first two coefficients of the Bergman function expansions for Cartan-Hartogs domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Zhiming Feng","submitted_at":"2018-04-13T10:49:29Z","abstract_excerpt":"Let $\\phi$ be a globally defined real K\\\"{a}hler potential on a domain $\\Omega\\subset \\mathbb{C}^d$, and $g_{F}$ be a K\\\"{a}hler metric on the Hartogs domain $ M=\\{(z,w)\\in \\Omega\\times\\mathbb{C}^{d_0}: \\|w\\|^2<e^{-\\phi(z)}\\}$ associated with the K\\\"{a}hler potential $\\Phi_{F}(z,w)=\\phi(z)+F(\\phi(z)+\\ln\\|w\\|^2)$. Firstly, we obtain explicit formulas of the coefficients $\\mathbf{a}_j\\;(j=1,2)$ of the Bergman function expansion for the Hartogs domain $( M,g_F)$ in a momentum profile $\\varphi$. Secondly, using explicit expressions of $\\mathbf{a}_j\\;(j=1,2)$, we obtain necessary and sufficient con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04880","kind":"arxiv","version":1},"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"}