{"paper":{"title":"On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kyunghwan Song, WonTae Hwang","submitted_at":"2019-04-05T13:35:37Z","abstract_excerpt":"We prove that the integer part of the reciprocal of the tail of $\\zeta(s)$ at a rational number $s=\\frac{1}{p}$ for any integer with $p \\geq 5$ or $s=\\frac{2}{p}$ for any odd integer with $p \\geq 5$ can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\\frac{2}{p},$ we use a result on the finiteness of integral points of certain curves over $\\mathbb{Q}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03060","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"}