{"paper":{"title":"The Spin $L$-function on $\\mathrm{GSp}_6$ via a non-unique model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Aaron Pollack, Shrenik Shah","submitted_at":"2015-03-27T19:36:15Z","abstract_excerpt":"We give two global integrals that unfold to a non-unique model and represent the partial Spin $L$-function on $\\mathrm{GSp}_6$. We deduce that for a wide class of cuspidal automorphic representations $\\pi,$ the partial Spin $L$-function is holomorphic except for a possible simple pole at $s=1$, and that the presence of such a pole indicates that $\\pi$ is an exceptional theta lift from $\\mathrm{G}_2$. These results utilize and extend previous work of Gan and Gurevich, who introduced one of the global integrals and proved these facts for a special subclass of these $\\pi$ upon which the aforement"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08197","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"}