{"paper":{"title":"On some mean square estimates for the zeta-function in short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2012-12-04T10:05:19Z","abstract_excerpt":"Let $\\Delta(x)$ denote the error term in the Dirichlet divisor problem, and $E(T)$ the error term in the asymptotic formula for the mean square of $|\\zeta(1/2+it)|$. If $E^*(t) = E(t) - 2\\pi\\Delta^*(t/2\\pi)$ with $\\Delta^*(x) =\n  -\\Delta(x) + 2\\Delta(2x) - 1/2\\Delta(4x)$ and we set $\\int_0^T E^*(t)\\,dt = 3\\pi T/4 + R(T)$, then we obtain $$ \\int_T^{T+H}(E^*(t))^2\\,dt \\gg HT^{1/3}\\log^3T $$ and $$ HT\\log^3T \\ll \\int_T^{T+H}R^2(t)\\,dt \\ll HT\\log^3T, $$ for $T^{2/3+\\epsilon}\\le H \\le T$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0660","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"}