{"paper":{"title":"On the proof of a variant of Lindel\\\"of's hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Athanassios S. Fokas","submitted_at":"2017-08-10T09:57:53Z","abstract_excerpt":"The leading asymptotic behaviour as $t\\to \\infty$ of the celebrated Riemann zeta function $\\zeta(s), \\ s = \\sigma + it, \\quad 0<\\sigma<1, \\quad t>0 , \\ t\\to\\infty,$ can be expressed in terms of a transcendental sum. The sharp estimation of this sum remains one of the most important open problems in mathematics with a long and illustrious history. Lindel\\\"of's hypothesis states that for $\\sigma=1/2$, this sum is of order $O\\left(t^\\varepsilon\\right)$ for every $\\varepsilon>0$. We have recently introduced a novel approach for estimating such transcendental sums: we have first embedded the Rieman"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06606","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"}