given a real function 'f' so the Fourier transform of f(x) exists and assuming Riemann Hypothesis is true so all the non-trivial zeros of Riemann Zeta are of the form 1/2+it then the Riemann-Weyl formula(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum _{t} f(t) = f(i/2)+f(-i/2)+2g(0)\pi- (2\pi)^{-1} \int_{-\infty}^{\infty}dr f(r) \frac{ \Gamma '(1/4+ir/2) }{\Gamma (1/4+ir/2)}+ \sum _{n=1}^{\infty} \Lambda (n) (n)^ {-1/2}g(lon) [/tex]

the first sum run over the non-trivial zeros, my question is if all the zeros are 1/2+it with 't' real number , the only condition for Riemann-Weyl formula to converge is that the Fourier transform of f(x) , which can be a function or a distribution must exists ? , under what conditions can be apply Riemann-Weyl summation formula? , if f(x) is a function g(u) is its Fourier transform

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# RIemann-Weyl formula and application

Loading...

Similar Threads for RIemann Weyl formula |
---|

I Geometric intuition of a rank formula |

**Physics Forums | Science Articles, Homework Help, Discussion**