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On the Number of Prime Numbers less than a Given Quantity
Источник пакета riemann.primes_1859 · Translation (c) D. R. Wilkins 1998, preliminary version December 1998
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- urn:doctrine:math:riemann-primes-1859#RIEMANN_1859_EN
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- Translation (c) D. R. Wilkins 1998, preliminary version December 1998
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- urn:doctrine:math:riemann-primes-1859#treatise
RIEMANN_1859_EN_TRANSLATION
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- urn:doctrine:math:riemann-primes-1859#RIEMANN_1859_EN_TRANSLATION
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- en
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- unofficial
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Публикации
| URI | Тип | documentHash | Получено |
|---|---|---|---|
| https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-translation.pdf | text/plain; charset=utf-8 | sha256:a167ba95adeca26f467ebb9713265f0e8fd58fd5da83a34d9ab42e1d1eee3ee1 | 2026-09-16T19:59:52Z |
Фрагменты — 3
p.5 · lemma
en · unofficial · sha256:a94cfe6b486201f85691e47f2d9d4b326581d5b8645da6adba3d663943e476b5EN
One now finds indeed approximately this number of real roots within these limits, and it is very probable that all roots are real. Certainly one would wish for a stricter proof here; I have meanwhile temporarily put aside the search for this after some fleeting futile attempts, as it appears unnecessary for the next objective of my investigation.p.1 · defn
en · unofficial · sha256:eb1725e30703b3db86377ea0b892c01b48faca504adc9c75837cad4ae242d8f8EN
On the Number of Prime Numbers less than a Given Quantity.
(Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse.)
Bernhard Riemann
Translated by David R. Wilkinsp.1 · defn
en · unofficial · sha256:3a4224ebccb21eede7b07287c136128169fbfc1fd3c05d3831fb3cedde9ce627EN
For this investigation my point of departure is provided by the observation of Euler that the product
Product 1/(1 - 1/p^s) = Sum 1/n^s,
if one substitutes for p all prime numbers, and for n all whole numbers. The function of the complex variable s which is represented by these two expressions, wherever they converge, I denote by zeta(s). Both expressions converge only when the real part of s is greater than 1; at the same time an expression for the function can easily be found which always remains valid.Хэш рядом с текстом — sha256 его точных байтов. Он и есть проверка того, что показанный текст совпадает с закреплённым в пакете: расхождение роняет статику оракула.