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Euler 1737 — Variae observationes circa series infinitas (E72)
chain
L. Euler (1737). Variae observationes circa series infinitas (E72). Comm. Acad. Sci. Petrop. 9 (1737, publ. 1744) 160–188. Canonical: https://scholarlycommons.pacific.edu/euler-works/72/. Free copy: https://scholarlycommons.pacific.edu/euler-works/72/. 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: the Euler product over the primes; its logarithm turns the product into a sum, and the sum of 1/p diverges like log log x.
source
card id
card_chain_euler_1737
address
WIT.codex.FCT/variae-observationes-circa-series-infinitas-e72/REF.WITNESSED@l-euler
adjoining cards
- builds on → Mercator 1668 — Logarithmotechnia — the Euler product over the primes; its logarithm turns the product into a sum, and the sum
- enables → Riemann 1859 — Über die Anzahl der Primzahlen unter einer gegebenen Grösse — zeta continued to the plane, the functional equation, the explicit formula through log zet
- part of → The Riemann chain - from Euler's product and Legendre's count to the critical line — a root of this chain - one of the two trees it began from
- enables → Dirichlet 1837 — Beweis des Satzes, dass jede unbegrenzte arithmetische Progression ... unendlich viele Primzahlen enthält — L-functions: Euler's product carried into arithmetic progressions
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