{"paper":{"title":"The Zeta Functions of Complexes from $\\Sp(4)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Chian-Jen Wang, Wen-Ching Winnie Li, Yang Fang","submitted_at":"2011-09-18T08:45:40Z","abstract_excerpt":"Let $F$ be a non-archimedean local field with a finite residue field. To a 2-dimensional finite complex $X_\\Gamma$ arising as the quotient of the Bruhat-Tits building $X$ associated to $\\Sp_4(F)$ by a discrete torsion-free cocompact subgroup $\\Gamma$ of $\\PGSp_4(F)$, associate the zeta function $Z(X_{\\Gamma}, u)$ which counts geodesic tailless cycles contained in the 1-skeleton of $X_{\\Gamma}$. Using a representation-theoretic approach, we obtain two closed form expressions for $Z(X_{\\Gamma}, u)$ as a rational function in $u$. Equivalent statements for $X_{\\Gamma}$ being a Ramanujan complex ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3854","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"}