{"paper":{"title":"Expansions of real numbers in non-integer bases and charaterisation of Lazy expansion of 1","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Vorashil Farzaliyev","submitted_at":"2024-11-27T01:02:19Z","abstract_excerpt":"In this paper, our main focus is expressing real numbers on the non-integer bases. We denote those bases as $\\beta$'s, which is also a real number and $\\beta \\in (1,2)$. This project has 3 main parts. The study of expansions of real numbers in such bases and algorithms for generating them will contribute to the first part of the paper. In this part, firstly, we will define those expansions as the sums of fractions with $1$'s or $0$'s in the nominator and powers of $\\beta$ in the denominator. Then we will focus on the sequences of $1$'s and $0$'s generated by the nominators of in the sums we me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10378","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/2412.10378/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"}