{"paper":{"title":"Solutions to certain 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":"2015-11-13T13:24:34Z","abstract_excerpt":"Denote by $\\text{PS}(\\alpha)$ the image of the Piatetski-Shapiro sequence $n \\mapsto \\lfloor n^{\\alpha} \\rfloor$ where $\\alpha > 1$ is non-integral and $\\lfloor x \\rfloor$ is the integer part of $x \\in \\mathbb{R}$. We partially answer the question of which bivariate linear equations have infinitely many solutions in $\\text{PS}(\\alpha)$: if $a, b \\in \\mathbb{R}$ are such that the equation $y=ax+b$ has infinitely many solutions in the positive integers, then for Lebesgue-a.e. $\\alpha > 1$, it has infinitely many or at most finitely many solutions in $\\text{PS}(\\alpha)$ according as $\\alpha < 2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04274","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":""},"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"}