{"paper":{"title":"Algebraicity of ratios of special $L$-values for $\\mathrm{GL}(n)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ankit Rai, Gunja Sachdeva","submitted_at":"2024-03-23T10:51:18Z","abstract_excerpt":"We prove, under certain assumptions, algebraicity of the ratio $L(m, \\Pi \\times \\chi)/L(m, \\Pi \\times \\chi')$, where $\\Pi$ is a cuspidal automorphic cohomological unitary representation of $\\mathrm{GL}_n(\\mathbb{A}_\\mathbb{Q})$, and $\\chi$, $\\chi'$ are finite order Hecke characters such that $\\chi_{\\infty} = \\chi'_{\\infty} = \\mathrm{sgn}^{r}$, and $m, r$ are specific positive integers which depends only on $\\Pi_{\\infty}$. The methods in this article are a generalization of those in the work of Mahnkopf [Cohomology of arithmetic groups, parabolic subgroups and the special values of $L$-function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.15795","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.15795/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"}