In this talk, we will give an overview of the Riemann zeta function and we will see some links between this function and the prime numbers. 

Then we will discuss an estimate for a discrete mean value of the Riemann zeta function and its derivatives multiplied by some Dirichlet polynomials. Assuming the Riemann Hypothesis, we will deduce a lower bound for the \(2k\)-th moment of all the derivatives of the Riemann zeta function evaluated at its nontrivial zeros.

This is based on a joint work with Kübra Benli and Nathan Ng.