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We present the asymptotics for the expectation (five terms plus an error), the second rising moment (six terms plus an error), and the variance of $T_{m}(N)$ (leading term), as well as its limit distribution as $N\\rightarrow \\infty$, when \\begin{equation*} p_{j}=\\frac{a_{j}}{\\sum_{j=2}"},"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":"1510.09045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-30T11:00:43Z","cross_cats_sorted":[],"title_canon_sha256":"2f163a6f99f183bd7036679285677d41c16fdda2285995510e454dde3719b61e","abstract_canon_sha256":"6c66d30e3b2b26eef9fb5c89fd4f3d72651c7f9ef9be3571c9b64c00eff32459"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:23.381430Z","signature_b64":"WSLa/Ow8dQEcR/j8kYiSXdY1JXZPAlXTCkjjUo+uZ9wlTINNXOFzDtbFA6lrTw3fehBd9RTuMZ0UCmpYzMgtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b53eb224fa863891dda7b154a9810e2344b85004836c965b7358311f11e0277","last_reissued_at":"2026-05-18T01:28:23.380606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:23.380606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The logarithmic Zipf version of the coupon collector's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aristides V. 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