{"paper":{"title":"On multiplicative recurrence along linear patterns","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Andreas Mountakis, Dimitrios Charamaras, Konstantinos Tsinas","submitted_at":"2024-12-04T17:45:49Z","abstract_excerpt":"In a recent article, Donoso, Le, Moreira and Sun studied sets of recurrence for actions of the multiplicative semigroup $(\\mathbb{N}, \\times)$ and provided some sufficient conditions for sets of the form $S=\\{(an+b)/(cn+d) \\colon n \\in \\mathbb{N} \\}$ to be sets of recurrence for such actions. A necessary condition for $S$ to be a set of multiplicative recurrence is that for every completely multiplicative function $f$ taking values on the unit circle, we have that $\\liminf_{n \\to \\infty} |f(an+b)-f(cn+d)|=0.$ In this article, we fully characterize the integer quadruples $(a,b,c,d)$ which satis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03504","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/2412.03504/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"}