{"paper":{"title":"Estimates of automorphic forms on $\\mathrm{SU}(n,1)$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CV","authors_text":"Anilatmaja Aryasomayajula, Baskar Balasubramanyam","submitted_at":"2024-06-11T18:13:42Z","abstract_excerpt":"For $n\\geq 2$, let $\\Gamma\\subset \\mathrm{SU}((n,1),\\mathcal{O}_{K})$ be a torsion-free, finite-index subgroup, where $\\mathcal{O}_K$ denotes the ring of integers of a totally imaginary number field $K$ of degree $2$. Let $\\mathbb{B}^n$ denote the $n$-dimensional complex ball endowed with the hyperbolic metric, and let $X_{\\Gamma}:=\\Gamma\\backslash \\mathbb{B}^n$ denote the quotient space. Furthermore, let $\\mu_{\\mathrm{hyp}}^{\\mathrm{vol}}$ denote the volume form associated to the hyperbolic metric. Let $\\Lambda:=\\Omega_{\\overline{X}_{\\Gamma}}^{n}$ denote the line bundle, where $\\overline{X}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07639","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.07639/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}