{"paper":{"title":"Weighted fourth moments of Hecke zeta functions with groessencharacters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nigel Watt","submitted_at":"2013-07-19T20:26:46Z","abstract_excerpt":"We use recently obtained bounds for sums of Kloosterman sums to bound the sum $\\sum_{-D\\leq d\\leq D} \\int_{-D}^D |\\zeta(1/2+it,\\lambda^d)|^4| \\sum_{0<|\\mu|^2\\leq M} A(\\mu)\\lambda^d((\\mu)) |\\mu|^{-2it}|^2 {\\rm d}t$, where $\\lambda^d$ is the groessencharacter satisfying $\\lambda^d((\\alpha)) = \\lambda^d(\\alpha{\\Bbb Z}[i]) = (\\alpha /|\\alpha|)^{4d}$, for $0\\neq\\alpha\\in{\\Bbb Z}[i]$, and $\\zeta(s,\\lambda^d)$ is the Hecke zeta function that satisfies $\\zeta(s,\\lambda^d) =(1/4)\\sum_{0\\neq\\alpha\\in{\\Bbb Z}[i]} \\lambda^d((\\alpha)) |\\alpha|^{-2s}$ for $\\Re(s)>1$, while the numbers $D,M\\in(0,\\infty)$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5333","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"}