https://mathworld.wolfram.com/RiemannZetaFunction.html

https://www.researchgate.net/post/Way_Riemann_Zeta_Function_is_Important

Dear Aziz Elghazouani

It gains its importance due to the strong relationship between the Riemann Zetta function and prime numbers distribution.

Also, it is one of the Millenium open problems.

The Riemann Hypothesis is

The nontrivial zeros of ζ(s) have a real part equal to 1/2.

See the attached file.

Best regards

hi.zeta(s=a+ib)=0 is important.

The Riemann Zeta function is very deeply connected to the distribution of the prime numbers. The error term in the prime number theorem is closely related to the position of the zeros of the Riemann Zeta function.

If the Riemann Hypothesis is true then the distribution of the prime numbers is definitely not random.