{"paper":{"title":"A Khintchine-type theorem and solutions to linear equations in Piatetski-Shapiro sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Glasscock","submitted_at":"2018-09-02T15:39:25Z","abstract_excerpt":"Our main result concerns a perturbation of a classic theorem of Khintchine in Diophantine approximation. We give sufficient conditions on a sequence of positive real numbers $(\\psi_n)_{n \\in \\mathbb{N}}$ and differentiable functions $(\\varphi_n: J \\to \\mathbb{R})_{n \\in \\mathbb{N}}$ so that for Lebesgue-a.e. $\\theta \\in J$, the inequality $\\| n\\theta + \\varphi_n(\\theta) \\| \\leq \\psi_n$ has infinitely many solutions. The main novelty is that the magnitude of the perturbation $|\\varphi_n(\\theta)|$ is allowed to exceed $\\psi_n$, changing the usual \"shrinking targets\" problem into a \"shifting targ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00360","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":""},"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"}