{"paper":{"title":"Vanishing, Unbounded and Angular Shifts on the Quotient of the Difference and the Derivative of a Meromorphic Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Lasse Asikainen, Risto Korhonen, Yu Chen","submitted_at":"2025-05-27T13:03:15Z","abstract_excerpt":"We show that for a vanishing period difference operator of a meromorphic function \\( f \\), there exist the following estimates regarding proximity functions, \\[ \\lim_{\\eta \\to 0} m_\\eta\\left(r, \\frac{\\Delta_\\eta f - a\\eta}{f' - a} \\right) = 0 \\] and \\[ \\lim_{r \\to \\infty} m_\\eta\\left(r, \\frac{\\Delta_\\eta f - a\\eta}{f' - a} \\right) = 0, \\] where \\( \\Delta_\\eta f = f(z + \\eta) - f(z) \\), and \\( |\\eta| \\) is less than an arbitrarily small quantity \\( \\alpha(r) \\) in the second limit. Then, under certain assumptions on the growth, restrictions on the period tending to infinity, and on the value di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21150","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/2505.21150/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"}