{"paper":{"title":"Pseudorandomness of the Ostrowski sum-of-digits function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lukas Spiegelhofer","submitted_at":"2016-11-09T18:42:30Z","abstract_excerpt":"For an irrational $\\alpha\\in(0,1)$, we investigate the Ostrowski sum-of-digits function $\\sigma_\\alpha$. For $\\alpha$ having bounded partial quotients and $\\vartheta\\in\\mathbb R\\setminus\\mathbb Z$, we prove that the function $g:n\\mapsto \\mathrm e(\\vartheta \\sigma_\\alpha(n))$, where $\\mathrm e(x)=\\mathrm e^{2\\pi i x}$, is pseudorandom in the following sense: for all $r\\in\\mathbb N$ the limit \\[\\gamma_r= \\lim_{N\\rightarrow\\infty}\\frac 1N\\sum_{0\\leq n<N}g(n+r)\\overline{g(n)} \\] exists and we have \\[\\lim_{R\\rightarrow\\infty}\\frac 1R\\sum_{0\\leq r<R}\\bigl\\lvert \\gamma_r\\bigr\\rvert^2=0.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03043","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"}