{"paper":{"title":"Similarity classes of integral $p$-adic matrices and representation zeta functions of groups of type $A_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Benjamin Klopsch, Christopher Voll, Nir Avni, Uri Onn","submitted_at":"2014-10-16T18:51:09Z","abstract_excerpt":"We compute explicitly Dirichlet generating functions enumerating finite-dimensional irreducible complex representations of various $p$-adic analytic and adelic profinite groups of type $\\mathsf{A}_2$. This has consequences for the representation zeta functions of arithmetic groups $\\Gamma \\subset \\mathbf{H}(k)$, where $k$ is a number field and $\\mathbf{H}$ a $k$-form of $\\mathsf{SL}_3$: assuming that $\\Gamma$ possesses the strong Congruence Subgroup Property, we obtain precise, uniform estimates for the representation growth of $\\Gamma$. Our results are based on explicit, uniform formulae for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4533","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"}