{"paper":{"title":"A hybrid Euler-Hadamard product and moments of \\zeta'(\\rho)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"H. M. Bui, Micah B. Milinovich, Steven M. Gonek","submitted_at":"2013-02-20T16:54:24Z","abstract_excerpt":"Keating and Snaith modeled the Riemann zeta-function \\zeta(s) by characteristic polynomials of random NxN unitary matrices, and used this to conjecture the asymptotic main term for the 2k-th moment of \\zeta(1/2+it) when k>-1/2. However, an arithmetical factor, widely believed to be part of the leading term coefficient, had to be inserted in an ad hoc manner. Gonek, Hughes and Keating later developed a hybrid formula for \\zeta(s) that combines a truncation of its Euler product with a product over its zeros. Using it, they recovered the moment conjecture of Keating and Snaith in a way that natur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5032","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"}