{"paper":{"title":"On holomorphic theta functions associated to rank $r$ isotropic discrete subgroups of a $g$-dimensional complex space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ahmed Intissar, Allal Ghanmi, Mohammed Souid El Ainin","submitted_at":"2015-06-21T11:45:48Z","abstract_excerpt":"We are interested in the $L^2$-holomorphic automorphic functions on a $g$-dimensional complex space $V^g_{\\mathbb{C}}$ endowed with a positive definite hermitian form and associated to isotropic discrete subgroups $\\Gamma$ of rank $2\\leq r \\leq g$. We show that they form an infinite reproducing kernel Hilbert space which looks like a tensor product of a theta Fock-Bargmann space on $V^{r}_{\\mathbb{C}}=Span_{\\mathbb{C}}(\\Gamma)$ and the classical Fock-Bargmann space on $V^{g-r}_{\\mathbb{C}}$. Moreover, we provide an explicit orthonormal basis using Fourier series and we give the expression of i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06353","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"}