{"paper":{"title":"On a hybrid fourth moment involving the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c, Wenguang Zhai","submitted_at":"2013-05-13T07:03:29Z","abstract_excerpt":"We provide explicit ranges for $\\sigma$ for which the asymptotic formula \\begin{equation*} \\int_0^T|\\zeta(1/2+it)|^4|\\zeta(\\sigma+it)|^{2j}dt \\;\\sim\\; T\\sum_{k=0}^4a_{k,j}(\\sigma)\\log^k T \\quad(j\\in\\mathbb N) \\end{equation*} holds as $T\\rightarrow \\infty$, when $1\\leq j \\leq 6$, where $\\zeta(s)$ is the Riemann zeta-function. The obtained ranges improve on an earlier result of the authors [Annales Univ. Sci. Budapest., Sect. Comp. {\\bf38}(2012), 233-244]. An application to a divisor problem is also given"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2685","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"}