{"paper":{"title":"On the behavior of the logarithm of the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shota Inoue","submitted_at":"2019-02-08T07:07:38Z","abstract_excerpt":"The purpose of the present paper is to reveal the relation between the behavior of the logarithm of the Riemann zeta-function $\\log{\\zeta(s)}$ and the distribution of zeros of the Riemann zeta-function. We already know some examples for the relation by some previous works. For example, Littlewood showed an upper bound of $\\log{\\zeta(1/2 + it)}$ by assuming the Riemann Hypothesis in 1924. One of our results reveals that Littlewood's upper bound can be proved without assuming a hypothesis as strong as the Riemann Hypothesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02956","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"}