{"paper":{"title":"On the partition function of the Riemann zeta function, and the Fyodorov--Hiary--Keating conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adam J. Harper","submitted_at":"2019-06-13T16:17:07Z","abstract_excerpt":"We investigate the ``partition function'' integrals $\\int_{-1/2}^{1/2} |\\zeta(1/2 + it + ih)|^2 dh$ for the critical exponent 2, and the local maxima $\\max_{|h| \\leq 1/2} |\\zeta(1/2 + it + ih)|$, as $T \\leq t \\leq 2T$ varies. In particular, we prove that for $(1+o(1))T$ values of $T \\leq t \\leq 2T$ we have $\\max_{|h| \\leq 1/2} \\log|\\zeta(1/2+it+ih)| \\leq \\log\\log T - (3/4 + o(1))\\log\\log\\log T$, matching for the first time with both the leading and second order terms predicted by a conjecture of Fyodorov, Hiary and Keating.\n  The proofs work by approximating the zeta function in mean square by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05783","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"}