{"paper":{"title":"Random multiplicative functions and typical size of character in short intervals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rachid Caich","submitted_at":"2024-02-09T14:15:07Z","abstract_excerpt":"We examine the conditions under which the sum of random multiplicative functions in short intervals, given by $\\sum_{x<n \\leqslant x+y} f(n)$, exhibits the phenomenon of \\textit{better than square-root cancellation}. We establish that the point at which the square-root cancellation diminishes significantly is approximately when the ratio $\\log\\big(\\frac{x}{y}\\big)$ is around $\\sqrt{\\log\\log x}$. By modeling characters by random multiplicative functions, we give a sharp bound of $\\frac{1}{r-1}\\sum_{\\chi \\!\\!\\!\\mod r} \\big|\\sum_{x<n\\leqslant x+y}\\chi(n)\\big|$, where $r$ is a large prime and $x+y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06426","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.06426/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}