{"paper":{"title":"On some upper bounds for the zeta-function and the Dirichlet divisor problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2015-08-26T07:50:10Z","abstract_excerpt":"Let $d(n)$ be the number of divisors of $n$, let $$ \\Delta(x) := \\sum_{n\\le x}d(n) - x(\\log x + 2\\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\\zeta(s)$ denote the Riemann zeta-function. Several upper bounds for integrals of the type $$ \\int_0^T\\Delta^k(t)|\\zeta(1/2+it)|^{2m}dt \\qquad(k,m\\in\\Bbb N) $$ are given. This complements the results of the paper Ivi\\'c-Zhai [Indag. Math. 2015], where asymptotic formulas for $2\\le k \\le 8,m =1$ were established for the above integral."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06394","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"}