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We study the error term of the general $m$-th Riesz mean of the arithmetical function $\\delta_k(n)$ for any positive integer $m \\ge 1$, namely the error term $E_m(x)$ where\n  \\[ \\frac{1}{m!}\\sum_{n \\leq x}\\delta_k(n) \\left( 1-\\frac{n}{x} \\right)^m = M_{m, k}(x) + E_{m, k}(x). \\] We establish a non-trivial upper bound for $\\left | E_{m, k} (x) \\right |$, for any integer $m\\geq 1$."},"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":"1609.06184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-20T14:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"a8c759bee2976accf1125de80b08e538d5b3033c0b4c99deaf32f5eca72ec70d","abstract_canon_sha256":"e576783062e6821519b5cfe2374fab4bad1de148a6ff5de9d2a6ec039a7398ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:40.577733Z","signature_b64":"neiybCKI6iHjkGRMrtK94n3oivUDT/buJCz03gMT4zIn0zAhVM2ogmiYId1H+wzOSYAZBFKvKcyeVebhWHMNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8755e67bd35f978d2c4f357d95086d1e9e2c765339ae7ca6bf952ceb2ab720e7","last_reissued_at":"2026-05-18T00:23:40.577088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:40.577088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Riesz means of $\\delta_k(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Saurabh Kumar Singh","submitted_at":"2016-09-20T14:04:49Z","abstract_excerpt":"Let $k\\geq 1$ be an integer. Let $\\delta_k(n)$ denote the maximum divisor of $n$ which is co-prime to $k$. 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