{"paper":{"title":"On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Manli Liu, Nan Li, Qiongyan Wang","submitted_at":"2020-05-06T10:26:20Z","abstract_excerpt":"In this paper, we prove that $\\zeta$ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in $\\Gamma, \\Gamma^{(n)}, \\Gamma^{(l)}$ over the ring of polynomials in $\\mathbb{C}$, $l>n\\geq 1$ are positive integers. We extended the result that $\\zeta$ does not satisfy any non-trivial algebraic differential equation whose coefficients are polynomials in $\\Gamma, \\Gamma', \\Gamma''$ over the field of complex numbers, which is proved by Li and Ye[7]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.02707","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.02707/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"}