{"paper":{"title":"On a cubic moment of Hardy's function with a shift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2015-11-23T09:04:47Z","abstract_excerpt":"An asymptotic formula for $$ \\int_{T/2}^{T}Z^2(t)Z(t+U)\\,dt\\qquad(0< U = U(T) \\le T^{1/2-\\varepsilon}) $$ is derived, where $$ Z(t) := \\zeta(1/2+it){\\bigl(\\chi(1/2+it)\\bigr)}^{-1/2}\\quad(t\\in\\Bbb R), \\quad \\zeta(s) = \\chi(s)\\zeta(1-s) $$ is Hardy's function. The cubic moment of $Z(t)$ is also discussed, and a mean value result is presented which supports the author's conjecture that $$ \\int_1^TZ^3(t)\\,dt \\;=\\;O_\\varepsilon(T^{3/4+\\varepsilon}). $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07140","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"}