痛苦一下
发表于 2025-3-23 12:31:53
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动脉
发表于 2025-3-23 15:25:43
,Towards Euler’s Product Formula and Riemann’s Extension of the Zeta Function,There is a very close connection between the sums of the reciprocals of the integers raised to a variable power that Euler wrote down in 1737, the now-called zeta function.
农学
发表于 2025-3-23 21:34:16
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Abominate
发表于 2025-3-23 23:01:41
Riemann as an Expert in Fourier Transforms,From here on we can directly arrive at Riemann’s main result of his 1859 paper. However, for the time being we have to accept two of Riemann’s novel quantities (details will be reported later): The entire function . (. is not an entire function) and the product formula for the . function.
Conscientious
发表于 2025-3-24 05:02:04
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PLE
发表于 2025-3-24 09:54:36
The Product Representation of , and , by Riemann (1859) and Hadamard (1893),Riemann’s goal (before Weierstrass!) was to prove that . can be expanded as an infinite product.
Oafishness
发表于 2025-3-24 13:59:41
,Derivation of von Mangoldt’s Formula for ,This is von Mangoldt’s formula for ., which contains essentially the same information as Riemann’s .. On the way to the explicit formula for ., we need a special representation of the discontinuity function.
nugatory
发表于 2025-3-24 16:42:40
The Number of Roots in the Critical Strip,The following theorem was originally formulated by Riemann—but not proved.
facetious
发表于 2025-3-24 20:42:16
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Fissure
发表于 2025-3-25 00:06:31
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