{"paper":{"title":"Uniformity and Functional Equations for Local Zeta Functions of $\\mathfrak{K}$-Split Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark Berman","submitted_at":"2008-02-28T13:46:02Z","abstract_excerpt":"We study the local zeta functions of an algebraic group $\\mathcal{G}$ defined over $\\mathfrak{K}$ together with a faithful $\\mathfrak{K}$-rational representation $\\rho$ for a finite extension $\\mathfrak{K}$ of $\\mathbb{Q}$. These are given by integrals over $\\mathfrak{p}$-adic points of $\\mathcal{G}$ determined by $\\rho$ for a prime $\\mathfrak{p}$ of $\\mathfrak{K}$. We prove that the local zeta functions are almost uniform for all $\\mathfrak{K}$-split groups whose unipotent radical satisfies a certain lifting property. This property is automatically satisfied if $\\mathcal{G}$ is reductive. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.4207","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":""},"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"}