{"paper":{"title":"On some mean value results for the zeta-function and a divisor problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivic","submitted_at":"2014-06-03T07:31:57Z","abstract_excerpt":"Let $\\Delta(x)$ denote the error term in the classical Dirichlet divisor problem, and let the modified error term in the divisor problem be $\\Delta^*(x) =\n  -\\Delta(x) + 2\\Delta(2x) - \\frac{1}{2}\\Delta(4x)$. We show that\n  $$\n  \\int_T^{T+H}\\Delta^*\\bigl(\\frac{t}{2\\pi}\\bigr)|\\zeta(1/2+it)|^2dt \\;\\ll\\; HT^{1/6}\\log^{7/2}T\n  \\quad(T^{2/3+\\varepsilon} \\le H = H(T) \\le T),\n  $$\n  $$\n  \\int_0^T\\Delta(t)|\\zeta(1/2+it)|^2dt \\;\\ll\\; T^{9/8}(\\log T)^{5/2},$$ and obtain asymptotic formulae for $$\n  \\int_0^T{\\Bigl(\\Delta^*\\bigl(\\frac{t}{2\\pi}\\bigr)\\Bigr)}^2 |\\zeta(1/2+it)|^2dt,\\quad\n  \\int_0^T{\\Bigl(\\Delt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0604","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"}