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We also show that $I_j$ is a rational polynomial the ordinary zeta values, and give explicit formulas for $j\\le 12$. As a byproduct, we obtain precise results about the convergence of norms of random variables and their moments. We study $\\Vert(U,1-U)\\Vert_n$ as $n$ tends to infinity and we also discuss $\\Vert(U_1,U_2,\\dots,U_r)\\Vert_n$ for standard uniformly distributed random var"},"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":"1802.09214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-26T09:28:49Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"70537cb763b5d39871cb8803a99a7b1640a4144c142cf175f609eb403156069f","abstract_canon_sha256":"1dea9b50b406d999098c475a016c4161207863c597c5d61a85afe3c8793f11a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:34.106540Z","signature_b64":"PPf5itCYUa8Ft3+Q0PGZ5aS+g/YpRnIKc9UeK758+Nw376v0F8ftRz0lwv4GJA/08SEzFPAfVyS8PKC6PlaMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8963a0bc2d08d4594ab39384d4ce7b735f68900841979a38e7f08014111f6b6","last_reissued_at":"2026-05-18T00:21:34.105835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:34.105835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Asymptotic Series for an Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.NT","authors_text":"Guy Louchard, Markus Kuba, Michael E. 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