{"paper":{"title":"On the Seventh Power Moment of $\\Delta(x)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinjiang Li","submitted_at":"2016-01-21T05:36:57Z","abstract_excerpt":"Let $\\Delta(x)$ be the error term of the Dirichlet divisor problem. In this paper, we establish an asymptotic formula of the seventh-power moment of $\\Delta(x)$ and prove that \\begin{equation*}\n  \\int_2^T \\Delta^7(x)\\mathrm{d}x=\n  \\frac{7(5s_{7;3}(d)-3s_{7;2}(d)-s_{7;1}(d))}{2816\\pi^7}T^{11/4}+O(T^{11/4-\\delta_7+\\varepsilon}) \\end{equation*} with $\\delta_7=1/336,$ which improves the previous result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05515","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"}