{"paper":{"title":"Testing the functional equations of a high-degree Euler product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David W. Farmer, Nathan C. Ryan, Ralf Schmidt","submitted_at":"2010-11-05T01:53:30Z","abstract_excerpt":"We study the L-functions associated to Siegel modular forms (equivalently, automorphic representations of ${\\rm GSp}(4,\\mathbb{A}_{\\mathbb{Q}})$) both theoretically and numerically. For the L-functions of degrees 10, 14, and 16 we perform representation theoretic calculations to cast the Langlands L-function in classical terms. We develop a precise notion of what it means to test a conjectured functional equation for an L-function, and we apply this to the degree 10 adjoint L-function associated to a Siegel modular form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1307","kind":"arxiv","version":1},"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"}