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We extend the range of V to V << (loglog T)^{1/10 - \\epsilon}. We also speculate on the size of the largest V for which this normal approximation can hold and on the correct approximation beyond that point."},"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":"1108.5092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-25T13:57:37Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e1aa096e4ca41213440a13e9a052bce00a324c13489891eefe424bc600abe762","abstract_canon_sha256":"656b7c8a20dbb66ec43a2d8bfefe733443d614226293cceb3850d12dc765e0ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:45.445924Z","signature_b64":"tUxLYcduRp5DQYLZFkfEMtk8fUcxKghUpUg9qEwkxXPCAqnt8JvNK5Qb6nVPCD2fMRLI0N1cvnNAaNyzCmcPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e0495d7969d0987b3f81ee628deb57c82fb7fdf068d1e0d9e495eb56e599d2e","last_reissued_at":"2026-05-18T04:14:45.445236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:45.445236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations in Selberg's central limit theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Maksym Radziwill","submitted_at":"2011-08-25T13:57:37Z","abstract_excerpt":"Following Selberg it is known that uniformly for V << (logloglog T)^{1/2 - \\epsilon} the measure of those t \\in [T;2T] for which log |\\zeta(1/2 + it)| > V*((1/2)loglog T)^{1/2} is approximately T times the probability that a standard Gaussian random variable takes on values greater than V. 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