{"paper":{"title":"On Weyl's asymptotics and remainder term for the orthogonal and unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Taheri, Chalres Morris","submitted_at":"2017-02-06T11:04:35Z","abstract_excerpt":"We examine the asymptotics of the spectral counting function of a compact Riemannian manifold by V.G.~Avakumovic \\cite{Avakumovic} and L.~H\\\"ormander \\cite{Hormander-eigen} and show that for the scale of orthogonal and unitary groups ${\\bf SO}(N)$, ${\\bf SU}(N)$, ${\\bf U}(N)$ and ${\\bf Spin}(N)$ it is not sharp. While for negative sectional curvature improvements are possible and known, {\\it cf.} e.g., J.J.~Duistermaat $\\&$ V.~Guillemin \\cite{Duist-Guill}, here, we give sharp and contrasting examples in the positive Ricci curvature case [non-negative for ${\\bf U}(N)$]. Furthermore here the imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01564","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"}