{"paper":{"title":"Generalizations of some results about the regularity properties of an additive representation function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Csaba S\\'andor, S\\'andor Z. Kiss","submitted_at":"2018-04-20T11:44:14Z","abstract_excerpt":"Let $A = \\{a_{1},a_{2},\\dots{}\\}$ $(a_{1} < a_{2} < \\dots{})$ be an infinite sequence of nonnegative integers, and let $R_{A,2}(n)$ denote the number of solutions of $a_{x}+a_{y}=n$ $(a_{x},a_{y}\\in A)$. P. Erd\\H{o}s, A. S\\'ark\\\"ozy and V. T. S\\'os proved that if $\\lim_{N\\to\\infty}\\frac{B(A,N)}{\\sqrt{N}}=+\\infty$ then $|\\Delta_{1}(R_{A,2}(n))|$ cannot be bounded, where $B(A,N)$ denotes the number of blocks formed by consecutive integers in $A$ up to $N$ and $\\Delta_{l}$ denotes the $l$-th difference. Their result was extended to $\\Delta_{l}(R_{A,2}(n))$ for any fixed $l\\ge2$. In this paper we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07560","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"}