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Let $(z_k)_{k\\in \\mathbb{N}}$ be the sequence of nontrivial zeros of $\\zeta(s)$ with positive imaginary part. We write $z_k= 1/2+i\\tau_k$ (RH says that these $\\tau_k$ are all real). Then the sequence $(\\tau_k)_{k\\in \\mathbb{N}},$ satisfies the following asymptotic relation \\[\\sum_{k\\in\\mathbb{N}}\\frac{2x}{x^2+\\tau_k^2}\\simeq \\frac12\\log\\frac{x}{2\\pi}+\\sum_{n=1}^\\infty \\frac{a_n}{x^n},\\,\\,x\\to +\\infty\\] where $a_{2n+1}=2^{-2n-2}(8-E_{2n})$, $a_{2n}=(1-2^{-2n+1})B_{2n}/(4n).$ Are there other sequences $","authors_text":"Juan Arias de Reyna, Yves Meyer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T19:54:26Z","title":"Asymptotic properties of zeros of Riemann zeta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07253","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9354d608d27c5ec4724b48bd447ec00caffe1590887761ff42efc79f2d70d41e","target":"record","created_at":"2026-07-05T11:34:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"43d65be9cd2a669cee567407656d34d074d0724f8fac0dffe1d701dd188f50f3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T19:54:26Z","title_canon_sha256":"30247deec57e3db9dcb7526aacbd38a3605dfb36c673b36a762c57248addf6a9"},"schema_version":"1.0","source":{"id":"2507.07253","kind":"arxiv","version":1}},"canonical_sha256":"b0c3529f06a78098b8a9d0d7e5dfda759b62674d47d867c5b8b185b311b7d0b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0c3529f06a78098b8a9d0d7e5dfda759b62674d47d867c5b8b185b311b7d0b0","first_computed_at":"2026-07-05T11:34:54.632084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:54.632084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9VmH74MG0o3WvVJo2Vh9I6M6yrwfKvcLImtbyHuXzDsoL9emz+NNhoOvTXEkrQBsUke3M2rMIAE5q6S0IcCHBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:54.632615Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.07253","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9354d608d27c5ec4724b48bd447ec00caffe1590887761ff42efc79f2d70d41e","sha256:87309f8f807bf67c76db8ec2ef95f4a8519a6cbe8b3561eecd60104aff67bb76"],"state_sha256":"6ebc3221b8ce88338b8569e9b146c4e54c332e26eb752e0624f188582316c6df"}