{"paper":{"title":"Invariant four-variable automorphic kernel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jayce R. Getz","submitted_at":"2014-10-27T23:21:18Z","abstract_excerpt":"Let $F$ be a number field, let $\\mathbb{A}_F$ be its ring of adeles, and let $g_1,g_2,h_1,h_2 \\in \\mathrm{GL}_2(\\mathbb{A}_F)$. Previously the author provided an absolutely convergent geometric expression for the four variable kernel function $$ \\sum_{\\pi} K_{\\pi}(g_1,g_2)K_{\\pi^{\\vee}}(h_1,h_2)L(s,(\\pi \\times \\pi^{\\vee})^S), $$ where the sum is over isomorphism classes of cuspidal automorphic representations $\\pi$ of $\\mathrm{GL}_2(\\mathbb{A}_F)$. Here $K_{\\pi}$ is the typical kernel function representing the action of a test function on the space of the cuspidal automorphic representation $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7458","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"}