{"paper":{"title":"Mean square of the error term in the asymmetric many dimensional divisor problem","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wenguang Zhai, Xiaodong Cao, Yoshio Tanigawa","submitted_at":"2015-01-18T06:52:15Z","abstract_excerpt":"Let $\\ba=(a_1,a_2,\\ldots,a_k)$, where $a_j \\ (j=1,\\ldots,k)$ are positive integers such that $a_1 \\leq a_2 \\leq \\cdots \\leq a_k$. Let $d(\\ba;n)=\\sum_{n_1^{a_1}\\cdots n_k^{a_k}=n}1$ and $\\Delta(\\ba;x)$ be the error term of the summatory function of $d(\\ba;n)$. In this paper we show an asymptotic formula of the mean square of $\\Delta(\\ba;x)$ under a certain condition. Furthermore, in the cases $k=2$ and 3, we give unconditional asymptotic formulas for these mean squares."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04270","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"}