{"paper":{"title":"Gowers norms of multiplicative functions in progressions on average","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xuancheng Shao","submitted_at":"2016-07-06T21:17:02Z","abstract_excerpt":"Let $\\mu$ be the M\\\"{o}bius function and let $k \\geq 1$. We prove that the Gowers $U^k$-norm of $\\mu$ restricted to progressions $\\{n \\leq X: n\\equiv a_q\\pmod{q}\\}$ is $o(1)$ on average over $q\\leq X^{1/2-\\sigma}$ for any $\\sigma > 0$, where $a_q\\pmod{q}$ is an arbitrary residue class with $(a_q,q) = 1$. This generalizes the Bombieri-Vinogradov inequality for $\\mu$, which corresponds to the special case $k=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01814","kind":"arxiv","version":2},"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"}