{"paper":{"title":"On the multiplicites of zeros of $\\zeta(s)$ and its values over short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2017-06-26T08:07:47Z","abstract_excerpt":"We investigate bounds for the multiplicities $m(\\beta+i\\gamma)$, where $\\beta+i\\gamma\\,$ ($\\beta\\ge \\1/2, \\gamma>0)$ denotes complex zeros of $\\zeta(s)$. It is seen that the problem can be reduced to the estimation of the integrals of the zeta-function over \"very short\" intervals. A new, explicit bound for $m(\\beta+i\\gamma)$ is also derived, which is relevant when $\\beta$ is close to unity. The related Karatsuba conjectures are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08268","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"}