- #1

eljose

- 492

- 0

[tex] \prod_{\sigma}(1-s/\sigma)e^{s/\sigma}=g(s) [/tex] where the product is over the non-trivial zeroes of Riemann function

then we take Logarithms to both sides so we have the equality:

[tex]Lng(s)=\sum_{\sigma}Ln(1-s/\sigma)+s/\sigma [/tex]

then we define the function M(x) in the way that gives the number of non trivial zeroes of riemann function up to x so how could we obtain using the same method that is applied to the product

[tex] \prod_p(1-p^{-s}) [/tex] ot get the integral equation for M(x)?...

this can be useful as if Riemann hypothesis is true we will have that M(z) is only non zero when Re(z)=1/2