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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 $"},"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":"2507.07253","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T19:54:26Z","cross_cats_sorted":[],"title_canon_sha256":"30247deec57e3db9dcb7526aacbd38a3605dfb36c673b36a762c57248addf6a9","abstract_canon_sha256":"43d65be9cd2a669cee567407656d34d074d0724f8fac0dffe1d701dd188f50f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:54.632615Z","signature_b64":"9VmH74MG0o3WvVJo2Vh9I6M6yrwfKvcLImtbyHuXzDsoL9emz+NNhoOvTXEkrQBsUke3M2rMIAE5q6S0IcCHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0c3529f06a78098b8a9d0d7e5dfda759b62674d47d867c5b8b185b311b7d0b0","last_reissued_at":"2026-07-05T11:34:54.632084Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:54.632084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic properties of zeros of Riemann zeta function","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Juan Arias de Reyna, Yves Meyer","submitted_at":"2025-07-09T19:54:26Z","abstract_excerpt":"We try to define the sequence of zeros of the Riemann zeta function by an intrinsic property. 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 $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07253","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.07253/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.07253","created_at":"2026-07-05T11:34:54.632146+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.07253v1","created_at":"2026-07-05T11:34:54.632146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07253","created_at":"2026-07-05T11:34:54.632146+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDBVFHYGU6AJ","created_at":"2026-07-05T11:34:54.632146+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDBVFHYGU6AJROFJ","created_at":"2026-07-05T11:34:54.632146+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDBVFHYG","created_at":"2026-07-05T11:34:54.632146+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW","json":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW.json","graph_json":"https://pith.science/api/pith-number/WDBVFHYGU6AJROFJ2DL6LX62OW/graph.json","events_json":"https://pith.science/api/pith-number/WDBVFHYGU6AJROFJ2DL6LX62OW/events.json","paper":"https://pith.science/paper/WDBVFHYG"},"agent_actions":{"view_html":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW","download_json":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW.json","view_paper":"https://pith.science/paper/WDBVFHYG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.07253&json=true","fetch_graph":"https://pith.science/api/pith-number/WDBVFHYGU6AJROFJ2DL6LX62OW/graph.json","fetch_events":"https://pith.science/api/pith-number/WDBVFHYGU6AJROFJ2DL6LX62OW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW/action/storage_attestation","attest_author":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW/action/author_attestation","sign_citation":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW/action/citation_signature","submit_replication":"https://pith.science/pith/WDBVFHYGU6AJROFJ2DL6LX62OW/action/replication_record"}},"created_at":"2026-07-05T11:34:54.632146+00:00","updated_at":"2026-07-05T11:34:54.632146+00:00"}