{"paper":{"title":"Multiple reciprocal sums and multiple reciprocal star sums of polynomials are almost never integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liping Yang, Min Qiu, Qiuyu Yin, Shaofang Hong","submitted_at":"2017-03-21T15:16:43Z","abstract_excerpt":"Let $n$ and $k$ be integers such that $1\\le k\\le n$ and $f(x)$ be a nonzero polynomial of integer coefficients such that $f(m)\\ne 0$ for any positive integer $m$. For any $k$-tuple $\\vec{s}=(s_1, ..., s_k)$ of positive integers, we define $$H_{k,f}(\\vec{s}, n):=\\sum\\limits_{1\\leq i_{1}<\\cdots<i_{k}\\le n} \\prod\\limits_{j=1}^{k}\\frac{1}{f(i_{j})^{s_j}}$$ and $$H_{k,f}^*(\\vec{s}, n):=\\sum\\limits_{1\\leq i_{1}\\leq \\cdots\\leq i_{k}\\leq n} \\prod\\limits_{j=1}^{k}\\frac{1}{f(i_{j})^{s_j}}.$$ If all $s_j$ are 1, then let $H_{k,f}(\\vec{s}, n):=H_{k,f}(n)$ and $H_{k,f}^*(\\vec{s}, n):=H_{k,f}^*(n)$. Hong an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07263","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"}