{"paper":{"title":"Linnik's problem for multiplicative functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Joni Ter\\\"av\\\"ainen, Kaisa Matom\\\"aki","submitted_at":"2026-05-27T01:44:41Z","abstract_excerpt":"We study a multiplicative function analogue of Linnik's problem on the least prime in an arithmetic progression. Let $h\\colon \\mathbb{N}\\to\\mathbb{R}\\setminus\\{0\\}$ be a multiplicative function, and let $a \\pmod q$ be a reduced residue class. We ask how far one must go before finding square-free integers $n_1,n_2\\equiv a \\pmod q$ with $h(n_1)<0<h(n_2)$. We show that one can always find such integers with $n_1,n_2\\le q^{2+o(1)}$, unless the sign of $h$ strongly pretends to be a real Dirichlet character modulo $q$. Thus, apart from this natural character obstruction, sign changes of a multiplica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27833","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/2605.27833/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"}