{"paper":{"title":"Algebraicity of ratios of Rankin-Selberg $L$-functions and applications to Deligne's conjecture","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shih-Yu Chen","submitted_at":"2022-05-30T18:56:24Z","abstract_excerpt":"In this paper, we prove Deligne's conjecture on the algebraicity of the critical values of symmetric power $L$-functions associated with modular forms of weight at least 5. We also establish new cases of Blasius' conjecture on the algebraicity of the critical values of tensor product $L$-functions associated with modular forms. Additionally, we prove an algebraicity result for the critical values of Rankin--Selberg $L$-functions for $\\GL_n \\times \\GL_2$ in the unbalanced case, which extends the previous results of Furusawa and Morimoto for ${\\rm SO}(V) \\times \\GL_2$. These results are applicat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.15382","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.15382/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}