{"paper":{"title":"The generalized Montgomery-Hooley formula: A survey","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Robert C. Vaughan","submitted_at":"2026-05-18T18:14:29Z","abstract_excerpt":"This memoir is a survey of theorems and inequalities which have grown out of, and extended, the seminal estimate of Montgomery \\cite{HM70} \\begin{multline*} V(x,Q)=\\sum_{q\\le Q}\\sum_{\\substack{a=1\\\\ (a,q)=1}}^q \\left| \\psi(x;q,a) - \\frac{x}{\\phi(q)} \\right|^2 \\\\ = Qx\\log x + \\textstyle O\\big(Qx\\log\\frac{2x}{Q}\\big) + O\\big(x^2(\\log x)^{-A}\\big)., \\end{multline*}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18996","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/2605.18996/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"}