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This generalizes the Bombieri-Vinogradov inequality for $\\mu$, which corresponds to the special case $k=1$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.01814","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-06T21:17:02Z","cross_cats_sorted":[],"title_canon_sha256":"0bd1553dcb32f1956ad6d7cc45577ab666f655b9b318574775ec6a82d78801d0","abstract_canon_sha256":"9aec947c4481bb3ac47641b46fa27eddbe576304197b4fe320fc87062bef0301"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:26.124414Z","signature_b64":"GfPyyFxNpRhrCO/AFQseIOy9xWcVvUBvvKUOm5vx6qxbS7E2A2qvoBAORCk7V7hZLJnsd++7kYOAwdzbNRABBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fdccc08a4918590d1fc6807ccae07ca9fa8ec487e82ea8d029a898b4cadbf4d","last_reissued_at":"2026-05-18T00:41:26.123803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:26.123803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $k \\geq 1$. 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