{"id": "card_chain_von_mangoldt_1905", "kind": "reference", "title": "Mangoldt 1905 — Zur Verteilung der Nullstellen der Riemannschen Funktion xi(t)", "body": "H. von Mangoldt (1905). Zur Verteilung der Nullstellen der Riemannschen Funktion xi(t). Math. Ann. 60 (1905) 1–19. DOI 10.1007/BF01447494. Canonical: https://doi.org/10.1007/BF01447494. Cited by its record. License as found: Springer TDM license — publisher's copyright, cited. What it gave the chain: N(T) = (T/2pi) log(T/2pi) - T/2pi + O(log T): Riemann's count of the zeros proven.", "source": {"label": "H. von Mangoldt (1905), Math. Ann. 60 (1905) 1–19", "url": "https://doi.org/10.1007/BF01447494", "domain": "mathematics", "authority_tier": "reference"}, "shelf": "codex", "box": "chain", "bands": ["chain", "record", "1905", "mangoldt", "mathematics"], "subject": "Zur Verteilung der Nullstellen der Riemannschen Funktion xi(t)", "connections": [{"to_card_id": "card_chain_riemann_1859", "relationship": "builds_on", "evidence": "N(T) = (T/2pi) log(T/2pi) - T/2pi + O(log T): Riemann's count of the zeros proven"}, {"to_card_id": "card_question_riemann", "relationship": "connects_at", "evidence": "where the logarithm enters: the zero count is (T/2pi) log(T/2pi) - sealed on the stick at the 100,000th zero"}, {"to_card_id": "card_chain_turing_1953", "relationship": "enables", "evidence": "Turing's method: the count of zeros below T checked by the argument, so a computation can certify"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.chain", "facets": {"subject": ["1905", "mangoldt", "mathematics", "record"]}, "presentation": {"glyph": "•", "kind_label": "chain", "by": "H. von Mangoldt (1905), Math. Ann. 60 (1905) 1–19", "authority": "reference", "posted": "", "standing": "", "link": {"url": "https://doi.org/10.1007/BF01447494", "host": "doi.org", "provider": "", "titled": "Mangoldt 1905 — Zur Verteilung der Nullstellen der Riemannschen Funktion xi(t)", "waybill_line": "", "reach": "", "embed": ""}}, "neighbors": [{"id": "card_chain_riemann_1859", "title": "Riemann 1859 — Über die Anzahl der Primzahlen unter einer gegebenen Grösse", "relationship": "builds on", "why": "N(T) = (T/2pi) log(T/2pi) - T/2pi + O(log T): Riemann's count of the zeros proven", "href": "/card/card_chain_riemann_1859", "resolved": true}, {"id": "card_question_riemann", "title": "The Riemann hypothesis", "relationship": "connects at", "why": "where the logarithm enters: the zero count is (T/2pi) log(T/2pi) - sealed on the stick at the 100,000th zero", "href": "/card/card_question_riemann", "resolved": true}, {"id": "card_chain_turing_1953", "title": "Turing 1953 — Some calculations of the Riemann zeta-function", "relationship": "enables", "why": "Turing's method: the count of zeros below T checked by the argument, so a computation can certify", "href": "/card/card_chain_turing_1953", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_chain_von_mangoldt_1905", "next_step": {"do": "read the source itself", "door": "FIND", "web": "/reader.html?card=card_chain_von_mangoldt_1905"}, "ends": "a verdict or a card · the trail · a seal · one next step"}}