let be the product:(adsbygoogle = window.adsbygoogle || []).push({});

[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

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

Dismiss Notice

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!

# Hadamard Product

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