{"paper":{"title":"Averages of diagonal Elliott-Halberstam problem twisted by M\\\"obius function with Sobolev and H\\\"older-Zygmund weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marco Cantarini","submitted_at":"2026-07-10T05:47:47Z","abstract_excerpt":"Recalling that the so-called Elliott-Halberstam conjecture twisted by the M\\\"obius function $\\mu(n)$ claims that \\[ \\sum_{q\\leq N^{\\theta}}\\max_{y\\leq N}\\max_{(a,q)=1}\\left|\\sum_{\\underset{{\\scriptstyle n\\equiv a\\,\\mod\\,q}}{n\\leq y}}\\Lambda(n)\\mu\\left(N-n\\right)-\\frac{1}{\\varphi\\left(q\\right)}\\sum_{n\\leq y}\\Lambda(n)\\mu\\left(N-n\\right)\\right|\\ll\\frac{N}{\\log\\left(N\\right)^{A}} \\] for every $A>0$, where $0<\\theta<1$ is fixed, and also recalling that the validity of this conjecture, in combination with the validity of the classical Elliott-Halberstam for suitable $\\theta$, proves the binary Gold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09110","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/2607.09110/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"}