{"paper":{"title":"On error sums formed by rational approximations with split denominators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carsten Elsner, Thomas Baruchel","submitted_at":"2016-02-20T20:00:03Z","abstract_excerpt":"In this paper we consider error sums of the form \\[\\sum_{m=0}^{\\infty} \\varepsilon_m\\Big( \\,b_m\\alpha - \\frac{a_m}{c_m}\\,\\Big) \\,,\\] where $\\alpha$ is a real number, $a_m$, $b_m$, $c_m$ are integers, and $\\varepsilon_m=1$ or $\\varepsilon_m ={(-1)}^m$. In particular, we investigate such sums for \\[\\alpha \\in \\big\\{ \\pi, e,e^{1/2},e^{1/3},\\dots, \\log (1+t), \\zeta(2), \\zeta(3) \\big\\} \\] and exhibit some connections between rational coefficients occurring in error sums for Ap\\'ery's continued fraction for $\\zeta(2)$ and well-known integer sequences. The concept of the paper generalizes the theory "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06445","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"}