{"paper":{"title":"On the modified Selberg integral of the three-divisor function $d_3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Coppola","submitted_at":"2011-06-25T09:05:43Z","abstract_excerpt":"We prove a non-trivial result for the,say,modified Selberg integral $\\modSel_3(N,h)$, of the divisor function $d_3(n):= \\sum_{a}\\sum_{b}\\sum_{c, abc=n}1$; this integral is a slight modification of the corresponding Selberg integral, that gives the expected value of the function in short intervals. We get, in fact, $\\modSel_3(N,h)\\ll Nh^2L^2$, where $L:=\\log N$; furthermore, as a byproduct, we obtain indications on the way in which it may be proved the weak sixth moment of the Riemann zeta function.(This was OLD abstract)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5696","kind":"arxiv","version":4},"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"}