{"paper":{"title":"On the values of representation functions II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Csaba Sandor, Quan-Hui Yang, Xing-Wang Jiang","submitted_at":"2019-04-23T14:23:53Z","abstract_excerpt":"For a set $A$ of nonnegative integers, let $R_2(A,n)$ and $R_3(A,n)$ denote the number of solutions to $n=a+a'$ with $a,a'\\in A$, $a<a'$ and $a\\leq a'$, respectively. In this paper, we prove that, if $A\\subseteq \\mathbb{N}$ and $N$ is a positive integer such that $R_2(A,n)=R_2(\\mathbb{N}\\setminus A,n)$ for all $n\\geq2N-1$, then for any $\\theta$ with $0<\\theta<\\frac{2\\log2-\\log3}{42\\log 2-9\\log3}$, the set of integers $n$ with $R_2(A,n)=\\frac{n}{8}+O(n^{1-\\theta})$ has density one. The similar result holds for $R_3(A,n)$. These improve the results of the first author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10352","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"}