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We get, in fact, $\\modSel_3(N,h)\\ll Nh^2L^2$, where $L:=\\log N$; furthermore, as a byproduct, we obtain indications on the way in which it may be proved the weak sixth moment of the Riemann zeta function.(This was OLD abstract)"},"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":"1106.5696","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-25T09:05:43Z","cross_cats_sorted":[],"title_canon_sha256":"24d6e450f250042822046130ecbaa1c7c268585ed09461dc4cd04a322ed99d59","abstract_canon_sha256":"3501f78b96623c4585711af2107d0e43e23a05a92d106f5b91641f3e34452d04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:10.831832Z","signature_b64":"CULiBN7DeTkHa1F8C9ZVQ7E1s929B5BJAvzlzQA+p8dCa/wViQ5o8CAAO239KbxrQ3/nc38NMWS/ffYQvo1sDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0c5b99657662c1710f70f7993a380bc53f9b4601a19420106b6d6058eaa7b3f","last_reissued_at":"2026-05-18T03:45:10.831286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:10.831286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the modified Selberg integral of the three-divisor function $d_3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Coppola","submitted_at":"2011-06-25T09:05:43Z","abstract_excerpt":"We prove a non-trivial result for the,say,modified Selberg integral $\\modSel_3(N,h)$, of the divisor function $d_3(n):= \\sum_{a}\\sum_{b}\\sum_{c, abc=n}1$; this integral is a slight modification of the corresponding Selberg integral, that gives the expected value of the function in short intervals. 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