{"id": "card_chain_dirichlet_1837", "kind": "reference", "title": "Dirichlet 1837 — Beweis des Satzes, dass jede unbegrenzte arithmetische Progression ... unendlich viele Primzahlen enthält", "body": "P. G. L. Dirichlet (1837). Beweis des Satzes, dass jede unbegrenzte arithmetische Progression ... unendlich viele Primzahlen enthält. Abh. Königl. Preuss. Akad. Wiss. (1837) 45–81. Cited by its record. License as found: public domain (the author died more than a century ago, or the work was published before 1930). What it gave the chain: L-functions: Euler's product carried into arithmetic progressions.", "source": {"label": "P. G. L. Dirichlet (1837), Abh. Königl. Preuss. Akad. Wiss. (1837) 45–81", "url": "", "domain": "mathematics", "authority_tier": "reference"}, "shelf": "codex", "box": "chain", "bands": ["chain", "record", "1837", "dirichlet", "mathematics"], "subject": "Beweis des Satzes, dass jede unbegrenzte arithmetische Progression ... unendlich viele Primzahlen enthält", "connections": [{"to_card_id": "card_chain_euler_1737", "relationship": "builds_on", "evidence": "L-functions: Euler's product carried into arithmetic progressions"}, {"to_card_id": "card_chain_riemann_1859", "relationship": "enables", "evidence": "zeta continued to the plane, the functional equation, the explicit formula through log zeta, and the hypothesis"}], "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": ["1837", "dirichlet", "mathematics", "record"]}, "presentation": {"glyph": "•", "kind_label": "chain", "by": "P. G. L. Dirichlet (1837), Abh. Königl. Preuss. Akad. Wiss. (1837) 45–81", "authority": "reference", "posted": "", "standing": ""}, "neighbors": [{"id": "card_chain_euler_1737", "title": "Euler 1737 — Variae observationes circa series infinitas (E72)", "relationship": "builds on", "why": "L-functions: Euler's product carried into arithmetic progressions", "href": "/card/card_chain_euler_1737", "resolved": true}, {"id": "card_chain_riemann_1859", "title": "Riemann 1859 — Über die Anzahl der Primzahlen unter einer gegebenen Grösse", "relationship": "enables", "why": "zeta continued to the plane, the functional equation, the explicit formula through log zeta, and the hypothesis", "href": "/card/card_chain_riemann_1859", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_chain_dirichlet_1837", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_chain_dirichlet_1837"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}