{"paper":{"title":"An experimental study of the monotonicity property of the Riemann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Yochay Jerby","submitted_at":"2017-07-03T07:13:08Z","abstract_excerpt":"In 1970, based on newly available empiric evidence, a remarkable monotonicity property for $| \\zeta(z) |$ was conjectured by R. Spira. The $\\zeta$-monotonicity property can be written as follows: $$ | \\zeta (x_2 + y i ) | < | \\zeta \\left ( x_1 +y i \\right )| \\hspace{0.5cm} \\textrm {for any } \\hspace{0.25cm} x_1 < x_2 \\leq 0.5 \\textrm{ and } 6.29 <y. $$ In this work we present an experimental study of the monotonicity conjecture, in the course of which new properties of $\\zeta(z)$ are discovered. For instance, the spectrum of semi-limits $ \\lambda(z) \\subset \\mathbb{R}$ and the core function $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01754","kind":"arxiv","version":8},"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"}