{"paper":{"title":"The $a$-values of the Riemann zeta function near the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Junsoo Ha, Yoonbok Lee","submitted_at":"2017-11-24T11:20:11Z","abstract_excerpt":"We study the value distribution of the Riemann zeta function near the line $\\Re s = 1/2$. We find an asymptotic formula for the number of $a$-values in the rectangle $ 1/2 + h_1 / (\\log T)^\\theta \\leq \\Re s \\leq 1/2+ h_2 /(\\log T)^\\theta $, $T \\leq \\Im s \\leq 2T$ for fixed $h_1, h_2>0$ and $ 0 < \\theta <1/13$. To prove it, we need an extension of the valid range of Lamzouri, Lester and Radziwi\\l\\l's recent results on the discrepancy between the distribution of $\\zeta(s)$ and its random model. We also propose the secondary main term for the Selberg's central limit theorem by providing sharper e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08928","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"}