{"paper":{"title":"Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Christopher Voll, Duong Hoang Dung","submitted_at":"2015-03-24T08:40:40Z","abstract_excerpt":"Let $G$ be a finitely generated torsion-free nilpotent group. The representation zeta function $\\zeta_G(s)$ of $G$ enumerates twist isoclasses of finite-dimensional irreducible complex representations of $G$. We prove that $\\zeta_G(s)$ has rational abscissa of convergence $a(G)$ and may be meromorphically continued to the left of $a(G)$ and that, on the line $\\{s\\in\\mathbb{C} \\mid \\textrm{Re}(s) = a(G)\\}$, the continued function is holomorphic except for a pole at $s=a(G)$. A Tauberian theorem yields a precise asymptotic result on the representation growth of $G$ in terms of the position and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06947","kind":"arxiv","version":3},"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"}