Titlebook: Reassessing Riemann‘s Paper; On the Number of Pri Walter Dittrich Book 20181st edition The Author(s) 2018 Riemann‘s Paper on Prime Numbers.

痛苦一下

動(dòng)脈

,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.

農(nóng)學(xué)

Abominate

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

PLE

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

,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

The Number of Roots in the Critical Strip,The following theorem was originally formulated by Riemann—but not proved.

facetious

Fissure