{"paper":{"title":"Unramified Godement-Jacquet theory for the spin similitude group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Aaron Pollack","submitted_at":"2017-04-19T19:04:58Z","abstract_excerpt":"Suppose $F$ is a non-archimedean local field. The classical Godement-Jacquet theory is that one can use Schwartz-Bruhat functions on $n \\times n$ matrices $M_n(F)$ to define the local standard $L$-functions on $\\mathrm{GL}_n$. The purpose of this partly expository note is to give evidence that there is an analogous and useful \"approximate\" Godement-Jacquet theory for the standard $L$-functions on the special orthogonal groups $\\mathrm{SO}(V)$: One replaces $\\mathrm{GL}_n(F)$ with $\\mathrm{GSpin}(V)(F)$ and $M_n(F)$ with $\\mathrm{Clif}(V)(F)$, the Clifford algebra of $V$. More precisely, we exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05897","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"}