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In a previous paper, the first-named author showed that if the members f and g of a Mobius pair are both finitely supported, then both functions vanish identically. Here we prove two significantly stronger versions of this uncertainty principle. A corollary is that in a nonzero Mobius pair, either \\sum_{n \\in supp(f)} 1/n or \\sum_{n \\in supp(g)} 1/n diverges."},"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":"1211.0189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-01T14:16:08Z","cross_cats_sorted":[],"title_canon_sha256":"df9ccd76f1a41d4197014f0d4125bcc96887c66c48ab2573f9c2ae195df15db0","abstract_canon_sha256":"f4c03296d82d6426a9b3a65cd6c10af5c2c8a0f1339fcabf0611c99c95333610"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:01.440727Z","signature_b64":"5r2oJ9IaDvXkaHcLRhHtS8IUeE+LRWLGKxnF1yZNLSsWFiCZqJ4hG0yiVW0Iff77+NlO13BVMSDUe6BaJPzJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19319e508fa0c8083e97f525a68df62e10158766bb018008bdb05ce8cef41629","last_reissued_at":"2026-05-18T02:39:01.440122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:01.440122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uncertainty principles connected with the M\\\"{o}bius inversion formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlo Sanna, Paul Pollack","submitted_at":"2012-11-01T14:16:08Z","abstract_excerpt":"We say that two arithmetic functions f and g form a Mobius pair if f(n) = \\sum_{d \\mid n} g(d) for all natural numbers n. 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