{"paper":{"title":"On the general additive divisor problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivic, Jie Wu (IECN)","submitted_at":"2011-06-23T14:46:35Z","abstract_excerpt":"We obtain a new upper bound for $\\sum_{h\\le H}\\Delta_k(N,h)$ for $1\\le H\\le N$, $k\\in \\N$, $k\\ge3$, where $\\Delta_k(N,h)$ is the (expected) error term in the asymptotic formula for $\\sum_{N < n\\le2N}d_k(n)d_k(n+h)$, and $d_k(n)$ is the divisor function generated by $\\zeta(s)^k$. When $k=3$ the result improves, for $H\\ge N^{1/2}$, the bound given in the recent work \\cite{[1]} of Baier, Browning, Marasingha and Zhao, who dealt with the case $k=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4744","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"}